COLLEGE  OF  AGRICULTURE 
DAVIS,  CALIFORNIA 


LIBRARY 


THE 

MECHANIC'S  TEXT-BOOK       . 

AND 

ENGINEER'S  PRACTICAL  GUIDE: 


CONTAINING 

A  CONCISE  TREATISE 

DN  THE  NATURE  AND  APPLICATION  OF  MECHANICAL  FORCES  ;   ACTION 
OF   GRAVITY;    THE  ELEMENTS    OF   MACHINERY;    RULES   AND 
TABLES  FOR  CALCULATING  THE  WORKING  EFFECTS  OF 
MACHINERY;   OF  THE  STRENGTH,  RESISTANCE, 
AND    PRESSURE   OF    MATERIALS;    WITH 
TABLES  OF  THE  WEIGHT  AND  COHE- 
SIVE   STRENGTH    OF    IRON 

AND    OTHER    METALS. 


COMPILED  AND  ARRANGED 

BY     THOMAS    KELT, 

"GLOUCESTER  CITY   MACHINE  COMPANY, 


TO   WHICH    IS    ADDED, 

VALUABLE     HINTS     TO    THE    YOUNG    MECHANIC     ON    THE    CHOICE 

OF    A     PROFESSION;      MISDIRECTION     OF    INDUSTRY; 

INTELI.ECTUAL     CULTIVATION,     AND     THE 

STUDIES    AND    MORALS    OF    THE 

MECHANIC,    ETC.,     ETC. 

BY   JOHN    FROST,    LL.   D. 


BOSTON: 
PHILLIPS,  SAMPSON,  AND  COMPANY. 

1857. 


Entered  according  to  Act  of  Cougrws.  in  the  year  1855 

BY    PHILLIPS.   SAMPSON   *    CO, 
In  the  Clerk's  Office  of  the  District  Court  of  Massachusetts 


CONTENTS. 


PRACTICAL  GEOMETRY. 
Theorems.  ***** 

To  erect  a  perpendicular  on  a  right  line, 9 

To  erect  a  perpendicular  at  tlio  end  of  a  line,..     9 

To  bisect  a  gi ven  an<jle, 10 

To  describe  a  circle  through  three  given  points 

out  of  a  right  line, 10 

To  find  the  centre  of  a  given  circle,.. 11 

To  find  the  length  of  any  given  arc  of  a  circle,   11 

To  draw  a  tangent  to  a  circle, 11 

To   draw   lines  toward   the  centre  of  a  circle, 

the  centre  being  inaccessible, 11 

To  describe  the  segment  of  a  circle, 12 

To  describe  an  ellipse,  or  oval, 13 

To  describe  an  elliptic  arch, 13 

To  describe  a  parabola, 14 

To  measure  an  inf*  icepted  line, 14 

To  find   the  distance  between  two  inaccessible 

objects, 15 

To  design  a  beam  of  strongest  section, 15 

To  obtain  the  distance  of  an  inaccessible  object,.  16 
To  find  the  proper  position  for  the  eccentric  in 

a  steam-engine, 16 

To  find  the  length  of  valve-levers, 16 

To  define  the  throw  of  an  eccentric,. 17 

To  describe  any  regular  polygon, 17 

To  construct  a  square  upon  a  right  line, 18 

To  form  a  square  equal  to  a  given  triangle,....  18 
To  form  a  square  equal  to  a  given  rectangle,  ..  18 
To  form  a  rectangle  equal  to  a  given  square,  ..  18 

To  bisect  any  given  triangle, 19 

To  describe  a  circle  in  a  given  triangle, 19 

To  form  a  rectangle  in  a  given  triangle, •  19 


/ 


6  •       CONTENTS. 

Table  of  Dimensions  for  Cast  Iron  Beams, 59 

To  find  the  weight  of  a  cast  iron  beam, 60 

Resistance  of  Bodies  to  Flexure  by  Vertical  Pressure,  GO 
To   determine   the   dimensions  of  a  column  to 

bear  a  given  pressure, 61 

Table  of  Dimensions  of  Cylindrical  Coin  inns  of  Cast 

/row, 62 

Resistance  of  Bodies  to  Twisting, 6iJ 

Relative  strength  of  metals  to  resist  torsion,...   64 

MECHANICS. 

Preliminary  Remarks, b4 

The  Lever, 65 

The  Wheel  and  dxle,  or  Crane. 

To   determine   the   amount* of  effective   power 
produced  from  a  given  power,  by  a  crane,.  ..   67 

Two  parts  of  a  crane  given,  to  find  the  third,..  68 

The  Pulley, '. 68 

Table  of  Inclined  Planes, 70 

Example  of  incline  and  velocity, 71 

Tlie  Wedge, 72 

The  Screw, 73 

CONTINUOUS   CIRCULAR   MOTION. 

When  Time  is  not  taken  into  Account. 

To  find  the  number  of  revolutions  of  the  last,  to 

one  of  the  first,  in  a  train  of  wheels  and  pinions,  75 
When  Time  must  be  regarded. 

The  distance  between  the  centres  and  velocities 

of  two  wheels  given,  to  find    their  diameters,  76 
To  d?termine  the  proportion  of  wheels  for  screw- 
cutting  by  a  lathe, 77 

Table  of  Change-  Wheels  for  Screw-cutting, 80 

Table  of  the  Pitch  of  Small  Wheels, 81 

Table  of  the  Strength  of  Teeth  of  Cast  Iron  Wheels,  .   81 

PRACTICAL   PROPERTIES   OF   WATER. 

Effects  produced  by  Water  in  its  natural  State,    8% 

To  find  the  velocity  of  water   issuing  a  circular 
orifice  at  any  given  depth  from  the  surface,..  83 


CONTENTS.  7 

STEAM   POWER. 

To  estimate  the  amount,  of  advantage  gained  by 

usiriif  strain  expansively  in  a  steam-engine,  .    88 
Effects  produced  by  Water  in  an  aeriform  State,   ....    90 

Table  of  the  Elastic  Force  of  Steam, 01 

Table  of  Boiling  Points, 93 

Elastic  Force  of  Steam  in  Inches  of  Mercury, 93 

Effects  produced  by  Air, 93 

Table  of  the  Expansion  of  Atmospheric  Air  by  Heat,  94 

Table  of  the  Quantity  of  Water  in  Pumps, 95 

Table  of  Force  and  Common  Appellations  of  Winds,.   97 

FRICTION. 
Laics  of  Friction, 98 

BOILERS   AND   THE   STEAM-ENGINE. 

Construction  of  Boilers, 100 

To  determine   the   proper  quantity  of  heating 

surface  in  a  boiler, 101 

To   determine    the    proper    dimensions    for   a 

wagon-shaped  boiler, 102 

To  determine  the  dimensions  for  a  cylindrical 

boiler, 102 

Specified  Particulars, 103 

Heating  Powers  of  Combustible  Substances, 103 

Table  of  Dimensiojis  for  Cylinders, 104 

PROPERTIES   OF   BODIES. 
Tables  of  the  Specific  Gravities  of  Bodies, 105-107 

PRACTICAL  TABLES. 

Weight  of  Square,  Round,  and  Flat  Bar  Ir on,.  .110-129 

Proportional  Breadth*  for  six-sided  Nuts  for  Bolts,.  130 

Weights  of  Sheet  Iron,  Copper,  and  Brass, 131 

Comparative  Weights  of  different  Bodies, 1 32 

Weights  of  Pipes  of  various  Metals,   133 

Weight  of  Cast  Iron  Bails, 134 

Mensuration  of  Timber. 

Flat  or  board  measure, . 135 

Cubic  or  solid  measure, 136 


8  CONTENTS 

Cast  Metal  Cylinders, 137 

Cast  Iron  Pipes, 1 38 

Compositions  of  Copper,  Tin,  and  Zinc, 139 

Degrees  of  Heat, 139 

LOGARITHMS. 

Utility  of  Logarithmic  Tables, 146 

To   find   the   logarithm  of  any  whole  number 

under  100, 147 

To  find  the  logarithm  of  any  number  between 

100  and  1000, I 147 

To  find  the  number  indicated  by  a  logarithm,.  148 

Table  of  Logarithms  from  1  to  100, li»0 

MISCELLANEOUS. 

Centres, 140 

Cohesion, "i 141 

Case- Hardening, 141 

Steam  Engines. 

To  estimate  the  effective  power  of  an  engine,  143 

To  determine  the  proper  velocity  for  a  piston,  143 

Table  of  approximate  velocities  for  pistons,  ..  144 

Parallel  motion  in  a  steam-engine, 144 

Table  of  distances  for  a  parallel  motion, 145 

Table  of  the  Quantity  and  Weight  of  Water  in  Pipes,  151 

Chtinvfs  induced  in  the  Structure  of  Iron, 152 

Strength  of  Journals  of  Shafts, 156 

Journals  of  First,  Movers, 1 58 

Strength  of  Wheels, 160 

Tables  of  Circumferences  and  rfreas  of  Circles,.  163-171 

Square  and  Cube  Roots  of  J\"umbers, 1 72 

Varnishes, 1 73 

Solders, 176 

Capacity  of  Cisterns, 1 77 

Screws,    177 

Weights  of  various  Substan'is, . .  178 


CONTENTS. 


PART  SECOND. 


INTRODUCTION. 


Page 


Choice,  of  a  Profession  —  Respectability  of  Met  Conical 

Trades, 179 

CHAPTER   I. 
The  Mechanic  should  be  Master  of  his  Trade, 186 

CHAPTER   II. 
The  Mechanic  should  remain  attached  to  his  Trade,     .    .  193 

CHAPTER   III. 
The  Mechanic  should  honor  his  Trade, 200 

CHAPTER   IV. 

The  Mechanic  should  devote  his  Leisure  to  the,  General 

Interests  of  his  Trade. 214 


CHAPTER  V. 
Misdirection  of  Industry  —  Prejudices  against  the  Me- 


chanical Trades, 


,216 


CHAPTER  VI. 

Intellectual  Cultivation  of  the  Mechanic  —  Its   Impor- 
tance,      222 

CHAPTER  VII. 

Means  of  Intellectual  Cultivation  accessible  to  the  Me- 
chanic,    .240 

CHAPTER  VIII. 

Rewards  of  Intellectual  Cultivation '»  accessible  to  the  Me- 
chanic,   247 


10  CONTENT*. 

CHAPTER   IX. 
The  3Iecha?itc-s  Studies, , 250 

CHAPTER   X. 
The  Mechanic's  Studies  continued, ^t>n 

CHAPTER   XI. 
The  Mer.ha?dc's  Studies  continued, 329 

CHAPTER   XII 
The  Mechanic's  Studies  continued,     .........  340 

CHAPTER   XIII. 
Tke  Mechanics  Studies  continued, 359 

CHAPTER   XJV. 
The  Morals  of  the  Mechanic, .   .  381 


THE  WORKSHOP  COMPANION. 


\ 


PRACTICAL  GEOMETRY. 

GEOMETRY  is  the  science  which  investigates  and 
demonstrates  the  properties  of  lines  on  surfaces  and 
solids;  hence,  PRACTICAL  GKOMKTKY  is  the  method 
of  applying  the  rules  of  the  science  to  practical  pur 
poses. 

1.  From  any  given  point,  in  a  straight  /{we,  to  erect  a 
perpendicular  ;  or,  to  make  a  line  at  right  angles  with  a 
given  line. 

On  each  side  of  the  point  A,  from 
which  the  line  is  to  be  mads,  take 
equal  distances,  as  A  6,  A  c  ,•  and 
from  6  and  c  as  centres,  with  any 
distance  greater  than  b  A,  or  c  A, 
describe  arcs  cutting  each  other  at 
d;  then  will  the  line  A  d  be  the  per- 
pendicular  required. 

2.  When  a  perpendicular  is  to  be  made  at  or  near  th* 
end  of  a  given  line. 

With  any  convenient  radius,  and 
with  any  distance  from  the  given  line 
A  6,  describe  a  portion  of  a  circle,  as 
b  A  c,  cutting  the  given  point  in  A  ; 
draw,  through  the  centre  of  th^  circle 
w,  the  line  b  n  c  ;  and  a  lin^  from  the 
p)int  A,  cutting  the  intersections  at  c, 
is  the  perpendicular  required. 


f 


10 


PRACTICAL   GEOMETRY. 


3.  To  do  the  same  otherwise. 

From  the  given  point  A,  with 
any  convenient  radius,  describe  the 
arc  d  c  b ;  from  d,  cut  the  arc  in  c, 
and  from  c,  cut  the  arc  in  b ;  also, 
from  c  and  b  as  centres,  describe 
arcs  cutting  each  other  in  / ;  then 
will  the  line  A  t  be  the  perpendic-  . 
ular  as  required. 


Note.  —  When  the  three  sides  of  a  triangle  are  in  the  propor- 
tion of  3,  4,  and  5  equal  parts,  respectively,  two  of  the  sides 
form  a  right  anirle;  and  observe  that  in  each  of  these  or  the 
preceding  problems,  the  perpendiculars  may  be  continued  be- 
low the  given  lines,  if  necessarily  required. 


4.  To  bisect  any  given  angle. 

From  the  point  A  as  a  centre,  with 
any  radius  less  than  the  extent  of  the 
angle,  describe  an  arc,  as  c  d;  and 
from  c  and  d  as  centres,  describe  arcs 
cutting  each  other  at  b ;  then  will 
the  line  A  6  bisect  the  angle  as  re- 
quired. 


5.  To  find  the  centre  of  a  circle,  or  radius,  that  shall 
cut  any  three  given  points,  not  in  a  direct  line. 

From  the  middle  point  6  as  a 
centre,  with  any  radius,  as  b  c,  b  d, 
describe  a  portion  of  a  circle,  as 
c  s  d;  and  from  r  and  t  as  centres, 
with  an  equal  radius,  cut  the  por- 
tion of  the  circle  in  c  s  and  d  s; 
draw  lines  through  where  the  arcs 
cut  each  other ;  and  the  intersection 
of  the  lines  at  s  is  the  centre  of  the 
circle  as  required. 


PRACTICAL   GEOMETRY. 


II 


6.  To  find  the  centre  of  a  given 
tircle. 

Bisect  any  chord  in  the  circle,  as 
A  B,  by  a  perpendicular,  C  D ;  bi- 
sect also  the  diameter  E  D  in  f; 
and  the  intersection  of  the  lines  at 
/  is  the  centre  of  the  circle  re- 
quired. 

7.  To  fnd  the  length  of  any  given 
arc  oj  a  circle. 

With  the  radius  A  C, 
equal  to  |th  the  length  of 
the  chord  of  the  arc  A  B, 
and  from  A  as  a  centre, 
cut  the  arc  in  c;  also  from  B  as  a  centre,  with  equal 
radius,  cut  the  chord  in  b;  draw  the  line  C  b;  and 
twice  the  length  of  the  line  is  the  length  of  the  arc 
nearly. 

8.  Through  any  given  point,  to  draw  a  tangent  to  a 
circle. 

Let  the  given  point  be  at  A; 
draw  the  line  A  C,  on  which 
describe  the  semicircle  ADC; 
draw  the  line  A  D  B,  cutting  the 
circumference  in  D,  which  is  the 
tangent  as  required. 


9.  To  draw  from  or  to  the  circumference  of  a  circle 
lines  tending  towards  the  centre,  when  the  centre  is  inac 
cessible. 

Divide  the  whole  or  any  given  portion  of  the  cir- 
cumference into  the  desired  number  of  equa    parts' 
then,  with  any  radius  less  than  the  distance  of  tw« 
2 


PRACTICAL    GEOMETRY. 


divisions,  describe   arcs  cutting  each  other,  as  A  1 


B  1,  C  2,  D  2,  &c.; 

draw  the  lines  C  1, 
B  2,  D  3,  &c.,  which 
lead  to  the  centre  as 
required. 


To  draw  the,  end  lines. 


As  A  r,  F  r,  from  C  describe  the  arc  r,  and  with  the 
radius  C  1,  from  A  or  F  as  centres,  cut  the  former  arcs 
at  r,  or  r,  and  the  lines  A  r,  F  r,  will  tend  to  the  centre 
as  required. 

10.  To  describe  an  arc,  or  segment  of  a  circle,  oj 
large  radii. 

Of  any  suitable  material,  construct  a  triangle,  as  A 
B  C;  make  A  B,  B  C,  each  equal  in  length  to  the 
chord  of  the  arc  D  E,  and  height,  twice  that  of  the  arc 


B  b.  At  each  end  of  the  chord  D  E  fix  a  pin,  and  at 
B,  in  the  triangle,  fix  a  tracer,  (as  a  pencil,)  move  the 
triangle  along  the  pins  as  guides ;  and  the  tracer  will 
describe  the  arc  required. 

11.  Or  otherwise. 

Draw  the  chord  A  C  B ;  also  draw  the  line  H  D 
I,  parallel  with  the 
chord,  and  equal  to 
the  height  of  the 
segment ;  bisect  the 
chord  in  C,  and 
erect  the  perpen- 
dicular C  D ;  join  A  D,  D  B ;  draw  A  H  perpendicular 
to  A  D,  and  B  I  perpendicular  to  B  D ,  erect  also  the 
perpendiculars  A  n,  B  n ;  divide  A  B  and  H  I  into  any 


PRACTICAL    GEOMETRY. 


J3 


number  of  equal  parts ;  draw  the  lines  1  1,  2  2,  3  3, 
fee. ;  likewise  divide  the  lines  A  ?i,  B  n,  each  into  half 
the  number  of  equal  parts ;  draw  lines  to  D  from  each 
division  in  the  lines  A  ?i>  B  n,  and,  through  where  they 
intersect  the  former  lines,  describe  a  curve,  which  will 
be  the  arc  or  segment  required. 

12.  To  describe  an  ellipse,  having  the  two  diameters 
given. 

On  the  intersection  of  the 
two  diameters  as  a  centre,  with 
a  radius  equal  to  the  difference 
of  the  semi-diameters,  describe 
the  arc  a  b ;  and  from  b  as  a 
centre,  with  half  the  chord  6  c  a, 
describe  the  arc  c  d ;  from  o,  as 
a  centre,  with  the  distance  o  d, 

cut  the  diameters  in  d  r,  d  t ;  draw  the  lines  r,  s,  s,  and 
£,  5,  s ;  then  from  r  and  t  describe  the  arcs  s,  s,  s,  s ; 
also  from  d  and  d,  describe  the  smaller  arcs  s,  s,  s,  s, 
which  will  complete  the  ellipse  as  required. 

13.  To  describe  an  elliptic  arch,  the  width  and  rise  of 
span  being  given. 

Bisect  with  a  line  at  right 
angles  the  chord  or  span  A 
B ;  erect  the  perpendicular  A 
g,  and  draw  the  line  q  D 
equal  and  parallel  to  A  C; 
bisect  A  C  and  A  q  in  r  and 
n ;  make  C  /  equal  to  C  D, 
and  draw  the  line  Irq;  draw 
also  the  line  n  s  D ;  bisect  8 
D  with  a  line  at  right  angles, 
and  meeting  the  line  C  D  in 
g ;  draw  thejine  g  q,  make  C  P  equal  to  C  &,  and  draw 
the  iine  g  P*i;  then  from  g  as  a  centre,  with  the  radius 
g-  D,  describe  the  arc  s  D  i ;  and  from  k  and  P  as  cen- 
tres, with  the  radius  A  k,  describe  the  arcs  A  8  and  B  ^ 
which  completes  the  arch  as  required.  O, 


14 


PRACTICAL   GEOMETRY. 


14.  Bisect  the  chord  A  B,  and  fix  at  right  angles  any 
straight  guide,  as  b  c ;  pre- 
pare, of  any  suitable  mate- 
rial, a  rod  or  staff',  equal  to 

half  the  chord's  length,  as 

d  e  f;  from  the  end  of  the 

stafij  equal  to  the  height 

of  the  arch,  fix  a  pin  e, 

arid  at  the    extremity  a 

tracer/;   move   the  staff, 

keeping   its    end    to    the 

guide  and  the  fixed  pin  to  the  chord ;  and  the  tracer 

will  describe  one  half  the  arc  required. 

15.  To  describe  a   parabola,  the  dimensions  being 
given. 

Let  A  B  equal  the  length,  and  C  D  the  breadth  of 
the  required  parabola ;  divide  C  A,  C  B  into  any  num- 


ber  of  equal  parts ;  also  divide  the  perpendiculars  A  a 
and  B  6  into  the  same  number  of  equal  parts;  then 
from  a  and  6  draw  lines  meeting  each  division  on  the 
line  A  C  B ;  and  a  curve  line  drawn  through  each  inter- 
section will  form  the  parabola  required. 

16.  To  obtain  by  measurement  the  length  of  any  direct 
line,  though  intercepted  by  some  material  object. 

Suppose  the 
distance  be- 
tween A  and  B 
is  required,  but 
the  right  line  is 
intercepted  by 
the  object  C. 
On  the  point  d, 
with  any  con- 


PRACTICAL    GEOMETRY. 


15 


renient  radius,  describe  the  arc  c  c,  make  the  arc  twice 
Che  radius  in  length,  through  which  draw  the  line  d  c  et 
and  on  e  describe  another  arc  equal  in  length  to  once 
the  radius,  as  eff;  draw  the  line  efr  equal  to  efd; 
on  r  describe  the  arc  jj,  in  length  twice  the  radius; 
continue  the  line  through  rj,  which  will  be  a  right 
line,  and  d  e,  or  e  r,  equal  the  distance  between  d  r 
by  which  the  distance  between  A  and  B  is  obtained  as 
required. 

17.  Jl  round  piece  of  timber  being  given,  out  of  which 
to  cut  a  beam  of  strongest  section. 

Divide  into  three  equal  parts  any 
diameter  in  the  circle,  as  Ac/,  e  C ; 
from  d  or  e,  erect  a  perpendicular 
meeting  the  circumference  of  the 
circle,  as  d  B ;  draw  A  B  and  B  C, 
also  A  D  equal  to  B  C,  and  D  C  equal 
to  A  B,  and  the  rectangle  will  be  a 
section  of  the  beam  as  required. 

18.  To  measure  the  distance  between  two  objects,  both 
being  inaccessible. 

From  any  point  C  draw  A 
any  line  C  c,  and  bisect  it 
in  D ;  take  any  point  E  in 
the  prolongation  of  A  C,  and 
draw  the  line  E  e,  making 
D  e  equal  to  D  E ;  in  like 
manner  take  any  point  F  in 
the  prolongation  of  B  C,  and 
make  D  /  equal  to  F  D. 
Produce  A  D  and  e  c  till 
they  meet  in  a,  and  also  B 
D  and  fc  till  they  meet  in 
6;  then  a  b  equal  A  B,  or 
the  distance  between  the 
objects  as  required. 
2* 


16 


PRACTICAL    GEOMETRY. 


19.  To  ascertain  the  distance,  geometrically,  of  anj 
inaccessible  object  on  an  equal  plane. 

Let  it  be  required  to  find  the 
distance  between  A  and  B,  A 
being  inaccessible;  produce  the 
line  in  the  direction  of  A  B  to 
any  point,  as  D ;  draw  the  line  D 
d  at  any  angle  to  the  line  A  B ; 
bisect  the  line  D  d,  through  which 
draw  the  line  B  b,  making  c  6 
equal  to  B  c  ,•  draw  the  line  d  b  a ; 
also  through  c,  in  the  direction  c 

A,  draw  the  line  a  c  A,  intersect- 
ing the  line  d  b  a  ;  then  b  a  equal 
B  A,  the  distance  required. 

20.  Otherwise. 

Prolong  A  B  to  any  point 
D,  making  B  C  equal  to  C 
D  ;  draw  the  line  D  a  at  any 
angle  with  D  A,  and  the  line 
C  b  similar  to  B  c;  draw  also 
the  line  .D  E  F,  which  inter- 
sects the  line  D  a ;  then  a  b  a- 
equal  B  A,  or  the  distance 
required. 

21.  To  find  the  proper  position  for  an  eccentric,  in 
relation  to  the  crank  in  a  steam  engine,  the  angle  oj 
eccentric  rod,  and  travel  of  the  valve,  being  given. 

Draw  the  right  line  A 

B,  as  the  situation  of  the 
crank   at  commencement 
of  the  stroke ;  draw  also 
the  line  C  d,  as  the  proper 
given  angle  of  eccentric 
rod  with  the  crank;  then 
from  C  as  centre,  describe 
a  circle  equal  to  the  travel 

of  the  ^alve ;  draw  the  line  e  f  at  right  angles  to  the  lino 


PRACTICAL   GEOMETRY. 


17 


C  J,  draw  also  the  lines  1  1,  and  2  2,  parallel  to  the  line 
e  f;  and  at  a  distance  from  e  /on  each  side,  equal  to  the 
.ap  and  lead  of  the  valve,  draw  the  angular  lines  C  1, 
C  2,  which  are  the  angles  of  eccentric  with  the  crank, 
for  forward  or  backward  motion,  as  may  be  required. 

22.  The  throw  of  an  eccentric,  and  the  travel  of  the 
valve  in  a  steam-engine,  also  the  length  of  one  lever  for 
communicating  motion  to  the  valve,  being  given,  to  deter- 
mine the  proper  length  for  the  other. 

On  any  right  line,  as  A  B,  describe  a  circle  A  D, 
equal  to  the  throw  a 

of  eccentric  and 
travel  of  valve ; 
then  from  C  as  a 
centre,  with  a  ra- 
dius equal  to  the 
length  of  lever 
given,  cut  the  line  A  B,  as  at  d,  on  which  describe  a 
circle,  equal  to  the  throw  of  eccentric  or  travel  of  valve, 
as  may  be  required ;  draw  the  tangents  B  a,  B  a,  cut 
ting  each  other  in  the  line  A  B,  and  d  B  is  the  length 
of  the  lever  as  required. 

Note.  —  The  throw  of  an  eccentric  is  equal  to  the  sum  of 
twice  the  distance   between  the  centres  of 
formation   and  revolution,  as  a  b,  or  to  the 
degree  of  eccentricity  it  is  made  to  describe, 
as  c  d.    And 

The  travel  of  a  valve  is  equal  the  sum  of 
the  widths  of  the  two  steam  openings,  and 
the  valve's  excess  of  length  more  than  just 
sufficient  to  cover  the  openings. 

23.  To  inscribe  any  regular  polygon  in  a  given  circle 
Divide  any  diameter,  as  A  B,  into 

so  many  equal  parts  as  the  polygon  is 
required  to  have  sides  ;  from  A  and  B 
as  centres,  with  a  radius  equal  to  the 
diametej,  describe  arcs  cutting  each 
other  in  C ;  draw  the  line  C  D  through 
the  second  point  of  division  on  the 
diameter  e,  and  the  line  D  B  is  one 
side  of  the  polygon  required. 


18 


PRACTICAL   GEOMETRY. 


24.  To  construct  a  square  upon  a  given  right  line. 

From  A  and  B  as  centres, 
with  the  radius  A  B,  describe 
Jie  arcs  A  c  6,  B  c  d,  and  from 
c,  with  an  equal  radius,  describe 
the  circle  or  portion  of  a  circle  d  [ 
t  d,  A  B,  6  c ;  from  b  d  cut  the 
circle  at  e  and  c ;  draw  the 
lines  A  e,  B  c,  also  the  line  s  t, 
which  completes  the  square  as 
required. 


a  given 


25.  To  form  a  square  equal  in  area   to 
triangle. 

Let  A  B  C  be  the  given  tri- 
angle ;  let  fall  the  perpendicu- 
lar B  d,  and  make  A  e  half  the 
height  d  B ;  bisect  e  C,  and  de- 
scribe the  semicircle  e  n  C ; 
erect  the  perpendicular  A  s,  or 
side  of  the  square,  then  A  5  t  x  is  the  square  of  equal 
area  as  required. 

26.  To  form  a  square  equal  in  area  to  a  given  rec- 
tangle. 

Let  the  line  A  B  equal  the  length  and  breadth  of 
the  given  rectangle ;  bisect  the 
line  in  e,  and  describe  the  semi- 
circle A  D  B;  then  from  A 
with  the  breadth,  or  from  B 
with  the  length,  of  the  rec- 
tangle, cut  the  line  A  B  at  C, 
and  erect  the  perpendicular  C  D,  meeting  the  curve  at 
D,  and  C  D  equal  a  side  of  the  square  required. 

27.  To  find  the  length  for  a  rectangle  whose  area  shall 
be  equal  to  that  of  a  given  square,  the  breadth  of  the  rec- 
tangle being  also  given. 

Let  A  B  C  D  be  the  given  square,  and  D  E  the  given 
breadth  of  rectangle ;  continue  the  line  B  C  to  F,  and 


PRACTICAL    GEOMETRY. 


19 


3SI 


draw  the  line  D  F ;  also, 

continue  the  line  D  C 

to  g,  and  draw  the  line 

A  g  parallel  to  D  F ; 

from  the  intersection  of 

the  lines  at  g,  draw  the 

line  g  d  parallel  to  D  E, 

and  E  d  parallel  to  D 

g-;  then  E  D  dg  is  the    A  I 

rectangle  as  required. 

28.  To  bisect  any  given  triangle. 

Suppose  ABC  the  given  triangle ; 
bisect  one  of  its  sides,  as  A  B  in  e, 
from  which  describe  the  semicirche 
A  r  B ;  bisect  the  same  in  r,  and 
from  B,  with  the  distance  B  r,  cut 
the  diameter  A  B  in  v ;  draw  the 
line  v  y  parallel  to  A  C,  which  will 
bisect  the  triangle  as  required. 


29.  To  describe  a  circle  of  greatest  diameter  in  a  giv- 
en triangle. 

Bisect  the  angles  A  and  B,  and  draw  the  intersecting 
lines  A  D,  B  D,  cutting 
each  other  in  D ;  then  from 
D  as  centre,  with  the  dis- 
tance or  radii  D  C,  de- 
scribe the  circle  C  e  y,  as 
required. 

30.  To  form  a  rectangle  of  greatest 
surface,  in  a  given  triangle. 

Let  ABC  be  the  given  triangle ; 
bisect  any  two  of  its  sides,  as  A  B,  B 
C,  in  e  and  d ;  draw  the  line  e  d;  also 
at  right  angles  with  the  line  e  d,  draw 
the  lines  ep,  dp,  and  epp  d  is  the  rec- 
tangle required. 


20 


DECIMAL  ARITHMETIC 

DECIMAL  ARITHMETIC  is  the  most  simple  and  ex 
plicit  mode  of  performing-  practical  calculations,  on 
account  of  its  doing  away  with  the  necessity  of  frac 
tional  parts  in  the  fractional  form,  thereby  reducing 
long  and  tedious  operations  to  a  few  figures  arranged 
and  worked  in  all  respects  according  to  the  usual  rules 
of  common  arithmetic. 

Decimals  simply  signify  tenths ;  thus,  the  decimal  of 
a  foot  is  the  tenth  part  of  a  foot,  the  decimal  of  that 
tenth  is  the  hundredth  of  a  foot,  the  decimal  of  that 
hundredth  is  the  thousandth  of  a  foot,  and  so  might  the 
divisions  be  carried  on  and  lessened  to  infinity ;  but  in 
practise  it  is  seldom  necessary  to  take  into  account  any 
degree  of  less  measure  than  a  one-hundredth  part  of 
the  integer  or  whole  number.  And,  as  the  entire  system 
consists  in  supposing  the  whole  number  divided  into 
tenths,  hundredths,  thousandths,  &c.,  no  peculiarity  of 
notation  is  required,  otherwise  than  placing  a  mark  or 
dot,  to  distinguish  between  the  whole  and  any  part  of 
the  whole ;  thus,  34-25  gallons  signify  34  gallons  2 
tenths  and  5  hundredths  of  a  gallon;  11-04  yards  sig 
nify  1 1  yards  and  4  hundredths  of  a  yard,  16-008  shil- 
lings signify  16  shillings  and  8  thousandth  parts  of  a 
shilling ;  from  which  it  must  appear  plain,  that  ciphers 
on  the  right  hand  of  decimals  are  of  no  value  whatever ; 
but  placed  on  the  left  hand,  they  diminish  the  decimal 
value  in  a  tenfold  proportion,  —  for  -6  signify  6  tenths ; 
•06  signify  6  hundredths;  and  -006  signify  6  thou- 
sandths of  the  integer,  or  whole  number. 

REDUCTION. 

Reduction  means  the  construing  or  changing  of  vul- 
gar fractions  to  decimals  of  equal  value ;  also  finding 
the  fractional  value  of  any  decimal  given. 

Rule  1.  Add  to  the  numerator  of  the  fraction  any 
number  of  ciphers  at  pleasure,  divide  the  sum  by  the 
denominator,  and  the  quotient  is  the  decimal  of  equiva- 
lent value. 


DECIMAL    ARITHMETIC.  21 

Rule  2.  Multiply  the  given  decimal  by  the  various 
fractional  denominations  of  the  integer,  or  whole  num 
ber,.  cutting  off  from  the  right  hand  of  each  product,  foi 
decimals,  a  number  of  figures  equal  to  the  given  number 
of  decimals,  and  thus  proceed  until  the  lowest  degree, 
or  required  value,  is  obtained. 

Ex.  1.  Required  the  decimal  equivalent,  or  decimal 
of  equal  value,  to  ^  of  a  foot 

—  —  -25,  the  decimal  required. 

Ex.  2.  Reduce  the  fraction  J  of  an  inch  to  a  deci 
inal  of  equal  value. 

-  —  —  '125,  the  decimal  required. 

8 

Ex.  3.  What  is  the  decimal  equivalent  to  5  of  a  gal 
Ion? 

-  ~-875,  the  decimal  equivalent. 

Ex.  4.  Required  the  fractional  value  of  the  decimal 
40625  of  an  inch. 

•40625 
Multiply  by  J  __  8 

3-25000 


•50000 

A  _  ? 

1-00000  i  and  fa  of  an  inch,  the  value 

required. 

Ex.  5.  What  is  the  fractional  value  of  -625  of  a 
cwt? 

•625 
Multiply  by  4  qrs,       4 

2-500 
X  28  Ibs.        28 

14-000  =  2  quarters  and  14  Ibs.,  the 
•  value  required. 


22  DECIMAL    ARITHMETIC. 

Ex.  6   Ascertain  the  fractional  value  of  -875  ot  ait 

imperial  gallon. 

•875 
Multiply  by  4  quarts 4 

3-500 
X  2  pints_ 

].()00  =  3  quarts  and  1  pint  the 
value  required. 

Ex.  7.  What  is  the  fractional  value  of  -525  ot  d  £. 
sterling  ? 

•525 
Multiply  by  20  sh._ 

10-500 
X  12  pence        j*j 

0-000  =  10  shillings  and  fi  pence* 
•  the  value  required. 


Independent  of  the  mark  or  dot  which  distinguishes 
between  integers  and  decimals,  the  fundamental  rules, 
viz.,  Addition,  Subtraction,  Multiplication,  and  Division, 
are  in  all  respects  the  same  as  in  Simple  Arithmetic ; 
and  an  example  in  each,  illustrative  of  placing  the 
separating  point,  will  no  doubt  render  the  whole  system 
sufficiently  intelligible,  even  to  the  dullest  capacity. 

Ex.  1.  Add  into  one  sum  the  following  integers  and 
decimals. 

16-625;  11-4;  20-7831;  12-125;  8-04;  and  7>00a 
1O625 
114 
207&31 
12-125 

8-04 

7.002 

75-9751  =  the  sum  required. 


DECIMAL    ARITHMETIC.  23 

Ex.  2.  Subtract  1  19-80764  from  234-98276 
234-98276 
119-80764 

115-1  75  12  z=  the  remainder 


Ex.  3.  Multiply  62-10372  by  16-732. 
62-10372 
16-732 

12420744 
18<J31116 
43472(504 
372<>22:*2 
6210372 


1039-1 1944304  —  the  product  required 


Observe  that  the  number  of  figures  in  the  product 
from  the  right  hand,  accounted  as  decimals,  are  equal 
to  the  number  of  decimals  in  the  multiplier  and  multi- 
plicand taken  together. 

Ex.  4.  Divide  39-375  by  9-25. 
l)-25 )  39  375  (4-256  =  the  quotient  required. 
3700 

2375         -Observe  that  the  number  of  dec! 

1850  male,  in  the  divisor  and  quotient 

together,  must  be  equal  to  the 
number  in  the  dividend. 


6250 
5550 

"  700 

Aivle.  —The  operation  might  be  still  continued,  so  as  to 
reduce  the  quotient  to  a  degree  of  greater  exactitude  ;  but  in 
practice  it  is  quite  unnecessary,  being  even  now  reduced  to  a 
measure  of  greater  nicety  than  is  commonly  required. 

3 


DECIMAL    ARITHMETIC. 


DEFINITIONS    OF    ARITHMETICAL    SIGNS 

EMPLOYED    IN     THE     FOLLOWING    CALCULATIONS,    WHICH 
OUGHT  TO  BE   PARTICULARLY    ATTENDED  TO 


£-9  i 


Tt     SO 

•8  + 


2    o  • 

*   £ 


I  x  -I  *  fc 

»  00     *#     —  0 

i  •*  £  s  °- 

*  -S    £    .S  .1 


J!  Ir  U  "PI 


ii  ^ 


e.  £   £  ••$ 


II 
I 

:i5 


"     -  i 

til 

ti     -    is 

s  -a  -« 

8--S 


"3    •?    ti   "•»     ?? 


rt     O 
•5     o 


HP 

co   g   £! 


*s  .£ 


U 

~    e 

£X     O 


Is- 


28^1. 


7«     »    -J 

2  |S 

5  «5  8 

3  2  2    II 

Tf 

«     -     -       X 


£ 
1 

I 


+  I  X  -I-  " 


u> 


a* 

£•1 

lo 


15 


DECIMAL    APPROXIMATIONS. 


POR  FACILITATING  CALCULATIONS  IN  MENSURATION. 


Uneal  feet  multiplied  by    -00019      = 
«      yards           "             -000568    = 
Square  inches         "              -007         = 
"      yards           «              -0002067  = 
Circular  inches       "              -OOaW5     = 
Cylindrical  inches  «              -0004545  =. 
"             feet      "             -02909     = 
Cubic  inches           "             -00058      = 

miles. 

square  feet, 
acres, 
square  feet, 
cubic  feet, 
cubic  yards, 
cubic  feet. 

"     feet 

« 

•03704 

= 

cubic 

yards. 

tt      a 

tt 

6-232 

— 

imper 

ial  gallons 

u    inches 

tt 

•003607 

= 

" 

M 

Cylindrical  feet 

tt 

4-895 

= 

n 

a 

"         inches 

u 

•002832 

= 

tt 

tt 

Cubic  inches 

« 

•263 

=  Ibs.  avs.   of  cast 

iron 

tt        tt 

't 

•281 

— 

tt 

wrought 

do. 

tt        tt 

it 

•283 

as 

tt 

steel.V 

tt         u 

tt 

•3225 

= 

u 

copper. 

u         tt 

u 

•3037 

sai 

tt 

brass. 

it         tt 

tt 

•26 

S3 

tt 

zinc. 

tt        tt 

tt 

.4103 

ss 

tt 

lead. 

it         tt 

tt 

•2636 

= 

« 

tin. 

•t          tt 

tt 

•4908 

= 

u 

mercury. 

Cylindrical  inches 

tt 

•2065 

SS 

tt 

cast  iron 

a 

tt 

•2168 

=r 

tt 

wrought 

iron 

u 

tt 

•2223 

=r 

tt 

steel. 

u 

tt 

'2533 

=r 

" 

copper. 

w 

tt 

•2385 

= 

« 

brass. 

a 

tt 

•201-2 

— 

« 

zinc. 

tt 

tt 

•3223 

ss 

tt 

lead. 

*                 «r 

*• 

207 

as 

tt 

tin. 

tt 

ft 

3854 

= 

tt 

mercury. 

Avoirdupois  Ibs. 

tt 

•009 

as 

cwts. 

tt 

tt 

•00045 

tt 

tens. 

DECIMAL    EQUIVALENTS. 


DECIMAL    EQUIVALENTS    TO    FRACTIONAL 
PARTS    OF    LINEAL    MEASURES. 


One  inch,  the  integer,  or  whole  number. 

•U6875         J  &  fa 

•625             ^ 

•28125        §  &  ^ 

•9375           1  &  T\j 

•59375         |  &  -rfe 

•25             ^ 

•90625         I  &  T& 

•5625           -|  &  TJF 

•21875        ^  &  7^ 

•875       o    F 

•53125   o    8  &  T-fV 

•1875     o  |&T^ 

•84375    -    J  &  $2 

•5          ^    ? 

•15625  "3  4-  &  -JJ2- 

•8125     |   f  &  A 

•46875    §•    4-  &  7^75- 

Oi        *£     O4-    O  ^ 

•125       1"  £ 

•78125   £    4  &  I$V 

'4375     g    ^&TV 

•09375   |           ^. 

.75     B  £ 

•40625         ^  &  ^j 

•0(525                   T!F 

•71875         |  &  JJ3J 

•375             f 

•03125                ^ 

•6875           |  &  T5 

•34375         |  &  gV 

•65625         |  &  -£2 

•3125           1  &  T^ 

One  foot,  or  12  inches,  the  integer. 

•9166         11  inches. 
•6333  -    10      *« 

•4166           5  inches. 
•3333     ^    4      «« 

•0625    c  |  of  inch. 
•0528    £  |      " 

•75      1     9      " 

•25         §    3      " 

•04  166  |  £       " 

•6666    Sf    8      " 

•1666     S"   2      " 

•03125  v  §       " 

•5833    £     7      " 

•0833      £     1       " 

•02083  |  |      " 

•5                6      « 

•07291    d    |       « 

•01041        ^       " 

One  yard,  or  36  inches,  the  integer. 

•972S        a«>  inches. 

•6389        23  inches. 

•3055       11  inches. 

•9445        34      " 

•61  11         22      " 

•2778       10      « 

•9167         33      " 

•5833         21       " 

'25            9      « 

•8889    c    32      " 

•5556    o    20      " 

•2222    o   8      « 

•8611    ~    31       " 

•5278  ^19      " 

•1944   ^    7       «{ 

•8333  |    30      " 

•5         =    18      " 

•1666    3   6       " 

•8056    5"  29      " 

•4722    »    17      " 

•1389    S"  5      " 

•7778    £    28      " 

•4445    |    16        « 

•1111    £   4      " 

•75       *    27      " 

•41%         15        « 

-0833    *   3      « 

•7232         26      " 

•3889         H        ' 

•0555         2      " 

•6944         25      " 

•3611          13        i 

•0277         1       «' 

•6667         24      " 

•3333         12        « 

j 

27 


MENSURATION. 

MENSURATION  is  that  branch  of  Mathematics  which 
IP  employed  in  ascertaining  the  extension,  solidities, 
and  capacities  "of  bodies,  capable  of  being  measured. 

1.    MENSURATION     OF    SURFACE. 

To  measure  or  ascertain  the  quantity  of  surface  in 
any  right-lined  figure  whose  opposite  sides  are  parallel  to 
iach  other,  as  a 

Square,        Rectangle,  Rhomboid, 

&c. 


Rule.  —  Multiply  the  length  by  the  breadth ;  the  pro- 
duct is  the  area  or  superficial  contents. 

Application  of  the  Rule  to  practical  Purposes. 

1.  The  side  of  a  square  piece  of  board  is  8T3^  inches 
fli  length  ;  required  the  area  or  superficies. 

Decimal  equivalent  to  the  fraction  ^  =  -1875,  (see  page  26 ;) 
and  8-1875  X  8-1875  =  67-03515625  square  inches,  the  area. 

2.  The  length  of  the  fire  grate  under  the  boiler  of  a 
steam  engine  is  4  feet  7  inches,  and  its  width  3  feet 

6  inches  ;  required  the  area  of  the  fire  grate. 

7  in.  =  -5833  and  6  in.  =  -5,  (see  Table  of  Equivalents,  p. 26;) 

hence  4-5833  X  3-5  =  16-04155  square  feet,  the  area. 

3.  Required  the  number  of  square  yards  in  a  floor 
whose  length  is  13£,  and  breadth  9|  feet 

13-5  x  9-75  =  131-625  -f  9  =  14-625  square  yards. 

Note  1.  —  The  above  rule  is  rendered  equally  applicable  to 
figures  whose  sides  are  not  parallel  to  each  other,  by  taking 


28  MENSURATION. 

the  mean  breadth  as  that  by  which  the  contents  are  to  be  esti- 
mated. 

2.  The  square  root  of  any  given  sum  equals  the  side  of 
square  of  equal  area. 

^3.  Any  square  whose  side  is  equal  to  the  diagonal  of  another 
square,  contains  double  the  area  of  that  square. 

4.  Any  sum  or  area,  (of  which  to  form  a  rectangle.)  divided 
by  tho  breadth,  the  quotient  equals  the  length  ;  or  divided  by 
the  length,  the  quotient  equals  the  breadth  of  the  rectangle, 
required. 

TRIANGLES. 

JJni/  two  sides  of  a  right-angled  triangle  being  gwtn^ 
to  full  the  third  side. 

Rule  1.  —  Add  together  the  squares  of  the  base  and 
perpendicular,  and  the  square  root  of  the  sum  is  tho 
hypotenuse  or  longest  side. 

Rule  2.  —Add  together  the  hypotenuse  a%nd  any  one 
side,  multiply  the  sum  by  their  difference,  and  the 
square  root  of  the  product  equals  the  other  side. 

Application  to  practical  Purposes. 

1.  Wanting  to  prop  a  building  with  rakingf  shores, 
the  top  ends  of  which  to  be  25  feet  from  the  ground, 
and  the  bottom  ends   16    feet  from  the   base  of  the 
building ;  what  must  be  their  length,  independent  of  any 
extra  length  allowed  below  the  surface  of  the  ground  ? 

252  +  162  =  V  881  =  29-6316  feet,  or  -6816x12  =  8  inches} 
consequently,  29  feet  8  inches  nearly. 

2.  From  the  top  of  a  wall  18  feet  in  height,  a  line 
was  stretched  across  a  canal  for  the  purpose  of  ascer- 
taining its  breadth ;  the  length  of  the  line,  when  meas- 
ured,   was  found  to  be  40  feet;  required  the  breadth 
from  the  opposite  embankment  to  the  base  of  the  wall. 


40  — 18  =  °2°2,  and  40  -f  18  x  22  =  V  1276  =  55-72,  or  35  feet 
9  inches  nearly,  the  width  of  the  can  il. 

Triangles  similar  to  each  other  are  proportional  to 
each  other;  hence  their  utility  in  ascertaining  tlia 
heights  and  distances  of  inaccessible  objects. 


MENSURATION. 


Thus,  suppose  the  height 
of  an  inaccessible  object  I)  is 
required ;  I  find  by  means  of 
two  staffs,  or  otherwise,  the 
height  of  the  perpendicular 
B  C  artd  the  length  of  the 
base  line  AB;  also  the  dis- 
tance from  A  to  the  base  of  the  object  G  D ; 

then  AB:  BC::AG.GD.     And  suppose  A  B  =  6  feet. 

B  C  =  2  feet,  and  A  G  =  150 
6  :  2  : :  150  :  50  feet,  the  height  of  D  from  G. 


Again,  suppose  the  inaccessible  dis- 
tance A  be  required ;  make  the  line  B  A, 
B  C,  a  right  angle,  and  B  C  of  three  or 
four  equal  parts  of  any  convenient  dis- 
tance, through  one  of  which,  and  in  a 
line  with  the  object  A,  determine  the 
triangle  CDF;  then  the  proportion  will 
be  as 


C  F  :  C  D  : :  B  F  :  B  A.     Let  C  F  =  10  yards,  C  D  =  53,  and 
B  F  =  30,  10  :  53  : :  30  :  159  yards,  the  distance  from  B. 

To  fnd  the  area  of  a  triangle  when  the  base  and  per- 
pendicular are  given. 

Rule.  —  Multiply    the   base    by    the   perpendicular 
weight,  and  half  the  product  is  the  area. 

1.  The  base  of  the  tri- 
anglo  A  D  B  is  11-3-  inches 
in  length,  and  the  height  D 
C,  3 1  inches ;  required  the 
jirea.  J 


hence 


-09375  and  f  =  -375,  (see  page  26  :) 

11-09375  X  3-375 

--  ^  -  =  18-72075  square  inches,  the  area. 


30  MENSURATION. 

2.  The  base  of  a  triangle  is  53  feet  3  inches,  and  the 
perpendicular  7  feet  9  inches  ;  required  the  area  or  su- 
perficies. 

53-25  x  7-75  _  ^.g^g  BqUare  feet,  the  area. 

Wlien  only  the  three  sides  of  a  triangle  can  be  given 
to  find  the  area. 

Rule.  —  From  half  the  sum  of  the  three  sides  subtract 
each  side  severally ;  multiply  the  half  sum  and  the 
three  remainders  together,  and  the  square  root  of  the 
product  is  equal  the  area  required. 

Required  the  area  of  a  triangle,  whose  three  sides 
are  respectively  50,  40,  and  30  feet 

50  4.  40  -f  30 

—          =  60,  or  half  the  sum  of  the  three  sides. 

60  —  30  =  30  first  difference, 
60  —  40  =  20  second  difference, 
60  —  50=  10  third  difference, 
then  30  X  20  X  10  X  60  =  V3&XXX)  =  600,  the  area  required. 

Triangles  are  employed  to 
great  advantage  in  deter- 
mining the  area  of  any  recti- 
lineal figure,  as  the  annexed, 
and  by  which  the  measure- 
ment is  rendered  compara- 
tively simple. 


POLYGONS. 

Polygons,  being  composed  of  triangles,  may  of  course 
be  similarly  measured;  hence,  in  regular  polygons, 
multiply  the  length  of  a  side  by  the  perpendicular 
height  to  the  centre,  and  by  the  number  of  sides,  and 
half  the  product  is  the  area. 


MENSURATION. 


I 

g 

I 


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fit   cS   TO   S   a&   ob    50    25 

i^       IO       ^?       X)       r-t       *O       !X       —  • 


—  *    ro    10 


oo 


'i'g  J  (M 

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C^     lO     O?  f^  IO     !"•* 

-to  J».OtO  OOt^C^t^ 

10     1^     00  ^     ?p     "^     Cp     l> 

i-^     1—1     r-i     rH 

o666AAA.A^ 

I^S       ^  ^  3  -  ^  - 

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1°    |     |    I   I   f    fill 
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32  MENSURATION. 

Application  of  the  Table. 

1.  The  radius  of  a  circle  being  6^  feet,  required  the 
side  of  the  greatest  heptagon  that  may  be  inscribed 
therein. 

•86.7  X  6-5  =  5-6355,  or  5  feet  7£  inches  nearly. 

2.  Each  side  of  a  pentagon  is  required  to  be  9  feet 
required  the  radius  of  circumscribing  circle. 

•852  X  9  =  7-668,  or  7  feet  8  inches. 

3.  A  perpendicular  from  the  centre  to  either  side  of 
an  octagon  is  required  to  be  12  feet;  what  must  be  the 
radius  of  circumscribing  circle? 

1-08  X  12  =  12-96,  or  12  feet  1 1J  inches. 

4.  Each  side  of  a  hexagon  is  4<|  yards ;  required  its 
superficial  contents. 

4i»  X  2-598  =  52-6095  square  yards. 


THE    CIRCLE    AND    ITS    SECTIONS. 

Observations  and  Definitions. 

1.  The  circle  contains  a  greater  area  than  any  other 
plane  figure  bounded  by  the  same  perimeter  or  out- 
line. 

2.  The  areas  of  circles  are  to  each  other  as  the 
squares  of  their  diameters;  any  circle  twice  the  diam- 
eter of   another  contains  four  times  the  area  of  the 
other. 

3.  The  radius  of  a  circle  is  a 
straight  line  drawn  from  the  centre 
to  the  circumference,  as  O  B. 

4.  The  diameter  of  a  circle  is  a 
straight   line   drawn    through  the 
centre,  and  terminated  both  ways 
at  the  circumference,  as  C  O  A. 

5.  A  chord  is  a  straight  line  joining  any  two  points 
of  the  circumference,  as  D  F. 

6.  The  versed  sine  is  a  straight  line  joining  the  chord 
and  circumference,  as  E  G. 


MENSURATION.  33 

7.  An  arc  is  a  ^y  part  of  the  circumference,  as  C  D  E. 

8.  A  semicircle  is  half  the  circumference  cut  oif  by 
a  diameter,  as  C  E  A. 

9.  A  segment  is  any  portion  of  a  circle  cut  off  by  a 
chord,  as  D  E  F. 

10.  A  sector  is  a  part  of  a  circle  cut  off  by  two  radii, 
as  A  O  B. 

General  Rules  in  Relation  to  the  Circle. 

1.  Multiply  the  diameter  by  3-1410,  the  product  is 
the  circumference. 

2.  Multiply  the  circumference  by  -31831,  the  product 
is  the  diameter. 

3.  Multiply  the  square  of  the  diameter   by  -7854, 
the  product  is  the  area. 

4.  Multiply  the  square  root  of  the  area  by  1-12837, 
the  product  is  the  diameter. 

5.  Multiply  the  diameter  by  -8862,  the  product  is  the 
side  of  a  square  of  equal  area. 

6.  Multiply  the  side  of  a  square  by  1-128,  the  prod- 
uct is  the  diameter  of  a  circle  of  equal  area. 

Application  of  Hie  Rules  as  to  Purposes  of  Practice. 

1.  The  diameter  of  a  circle  being  7T\  inches,  re 
quired  its  circumference. 

7-1875  X  3-1416  =22-58025  inches,  the  circumference. 
Or,  the  diameter  being  30£  feet,  required  the  circum- 
ference. 

3-1416  X  30-5  =  95-8188  feet,  the  circumference. 

2.  A  straight  line,  or  the  circumference  of  a  circle, 
oeing  274-89  inches,  required  the  circle's  diameter  cor- 
responding thereto. 

274-89  X  '31831  =  87-5  inches  diameter. 

-Or,  what  is  the  diameter  of  a  circle,  when  the  cir- 
cumference is  39  feet  ? 

31831  X  39  =  12-41409  feet,  and  41409  X  12  =  4-96908  inches, 
or  12  feet  5  inches,  very  nearly  the  diameter. 


34  MENSURATION. 

3.  The  diameter  of  a  circle  is  31  inches  ;  what  j"  its 
area  Jr.  square  inches  ? 

3-75'  =  14.-M25  X  -7&H  =  1  1-044,  &c.,  inches  area. 
Or,  suppose  the  diameter  of  a  circle  25  feet  G  inc.best 
required  the  area. 

2.V5'-'  =  fioO-25  X  -7854  =  510-706,  &c.,  fe^t.  the  arna. 

4.  What  must  the  diameter  of  a  circle  be,  to  contain 
an  area  equal  to  7U(rri(J  square  inches  ? 


V  706:86~=  26-5U>  X  H2837  =  29-998  or  30  inches,  the  diam- 
eter  required. 

5.  The  diameter  of  a  circle  is  144  inches;  what  must 
I  make  each  side  of  a  square,  to  be  equal  in  area  to  the 
given  circle  ? 

14--25  X  -8862=  12-62335  inches,  length  of  side  required. 

./?n?y  chord  and  versed  sine  of  a  circle  being  given,  to 
find  tJte  diameter. 

Rule.  —  Divide  the  sum  of  the 
squares  of  the  chord  and  versed  sine 
by  the  versed  sine,  the  quotient  is 
the  diameter  of  corresponding  circle. 

1.  The  chord  of  a  circle  A  B 
equal  ty  feet,  and  the  versed  sine 
C  D  equal  2  feet,  required  the  cir- 
cle's diameter. 


6-0*  4-  22  =  46-25  -f.  2  =  23-125  feet,  the  diameter. 

2.  In  a  curve  of  a  railway,  I  stretched  a  line  72  feet 
m  length,  and  the  distance  from  the  line  to  the  curve  1 
found  to  be  l\  ft.  ;  required  the  radius  of  the  curve. 

722  -f  1-252  =  5185-5625,  and 


i'^O  X  -^ 

Tojind  the  length  of  any  given  arc  of  a  circle. 

Rule.  —  From  eight  times  the  chord  of  half  the  arc 
subtract  the  chord  of  the  whole  arc,  and  one  third  of 
{he  remainder  is  equal  the  length  of  the  arc. 


MENSURATION.  35 

Required  the  length 
of  the  arc  ABC,  the 
chord  A  B  of  half  the 
arc  being  4  feet  3  inches, 
and  chord  A  C  of  the  whole  arc  8  feet  4  inches. 


=  34,andM  — 8-333==— -  =  8-555  feet,  the 
length  of  the  arc. 

To  find  the  area  of  Hue  sector  of  a  circle. 

Rule.  —  Multiply  the  length  of  the  arc  by  its  radius, 
and  half  the  product  is  the  area. 

The  length  of  the  arc  ACS, 
equal  9£  feet,  and  the  radii  F  A, 
F  B,  equal  each  7  feet,  required  the 
area. 

9-5  X  7  =  65-5  -f  2  =  32-75,  the  area. 

Note.  —  The  most  simple  means  where- 
by to  find  the  area  of  the  segment  of  a 


circle  is,  to  first  find  the  area  of  a  sector 

whose  arc  is  equal  to  that  of  the  given 

segment  5  and  if  it  toe  less  than  a  semicircle,  subtract  the  area 

of  the  triangle  formed  by  the  chord  of  the  segment  and  radii 

of  its  extremities  ;  but  if  more  than  a  semicircle,  add  the  area 

of  the  triangle  to  the  area  of  the  sector,  and  the  remainder,  or 

sum,  is  the  area  of  the  segment. 

Thus,  suppose  the  area  of  the  segment  A  C  B  e  is  required, 
and  that  the  length  of  the  arc  A  C  B  equal  9|  feet,  F  A  and 
F  B  each  equal  7  feet,  and  the  chord  A  B  equal  8  feet  4 
inches,  also  the  perpendicular  e  F  equal  3|  feet. 

9-75x7  =3fr|25  feet^  the  area  of  the  gector 

vx       .' 

15-624  feet,  area  of  the  triangle. 


-  —- 
And  34-125  —  15-624  =  18-501  feet,  the  area  of  the  segment. 

To  fnd  the  area  of  the  space  contained  between  two 
concentric  circles. 

Rule.  —  Multiply  the  sum  of  the  inside  and  outside 
diameters  by  their  difference,  and  by  '7854,  the  product 
is  the  area. 

4 


36  MENSUIIAT10N. 

1.  Suppose  the  external  circle 
A  B  equal  32  niches,  and  internal 
circle  C  D  equal  28  inches ;  re- 
quired the  area  of  the  space  con- 
tained between  them. 


32  +  28  =  60,  and  3°2  —  28  =  4,  hence 
60  X  4  X  -7854=188-496  in.,  the  area. 

2.  The  exterior  diameter  of  the  fly-wheel  of  a  steam 
engine  is  20  feet,  and  the  interior  diameter  18£  feet; 
required  the  area  of  the  surface  or  rim  of  the  wheel. 

-20+13-5  =  38-5  and  20—18-5  =1-5,  hence  38-5  X  1-5  x  -7854 
=  45-35,  &c.,  feet,  the  area. 

To  find  the  area  of  an  ellipsis  or  oval. 

Rule.  —  Multiply  the  longest  diameter  by  the  short- 
est, and  the  product  by  -7854  ;  the  result  is  the  area. 

An  oval  is  25  inches  by  16-5 ;  what  are  its  superficial 
contents  ? 

25  X  16-5  =  412-5  x  '7854  =  323-9775  inches,  the  area. 

Note.  —  Multiply  half  the  sum  of  the  two  diameters  by 
3*1416,  and  the  product  is  the  circumference  of  the  oval  or 
ellipsis. 

To  find  the  area  of  a  parabola,  or  its  segment. 

Rule.  —  Multiply  the  base  by  the  perpendicular 
height,  and  two  thirds  of  the  product  is  the  area. 

What  is  the  area  of  a  parabola  whose  base  is  20  feet 
and  height  12  ? 

240  v  2 
20  X  12  =  — f—  =  160  feet,  the  area. 

o 

Note. — Although  the  whole  of  the  preceding  practical  appli- 
cations or  examples  are  given  in  measures  of  feet  or  inches, 
these  being  considered  as  the  most  generally  familiar,  yet  the 
rules  are  equally  applicable  to  any  other  unit  of  measurement 
whatever,  as  yards,  chains,  acres,  &c.  &c.  &c. 


BIENSURATION.  37 

2.    MENSURATION    OF  THE   SUPERFICIES,   SOLID 
ITIES,    AND    CAPACITIES    OF    BODIES. 

7V?  find  the  solidity  or  capacity  of  any  figure  in  the 
vibical  form. 

Rule.  —  Multiply  the  length  of  any  one  side  by  ita 
breadth  and  by  the  depth  or  distance  to  its  opposite 
aide ;  the  product  is  the  solidity  or  capacity,  in  equal 
terms  of  measurement. 

Application  of  the  Rule  to  practical  Purposes. 

1.  Required  the  number  of  cubic  inches  in  a  piece 
of  timber  2-{£  inches  long,  7|   inches  broad,  and  3| 
inches  in  thickness. 

23-5  X  7-75  x  3-625  =  660-203  cubic  inches. 

2.  A  rectangular  cistern   is   in  length   8£   feet,  in 
breadth  54  feet,  and  in  depth  4  feet;  required  its  ca- 
pacity in  cubic  feet,  also  its  capacity  in  British  impe- 
rial gallons. 

8-5  x  5-25  x  4  =  178-5  cubic  feet,  and  178-5  x  6-232  (see  Table 
of  Decimal  Approximations,  p.  25)  =  1112-412  gallons. 

3.  A  rectangular  cistern,  capable  of  containing  520 
imperial  gallons,  is  to  be  7\  feet  in  length,  and  4£  feet 
in  width;  it   is  required  to  ascertain  the   necessary 
depth. 

520-000 

7-25  x  4-5  X  6-232  =  203-318.  and =  2-557  feet,  or  2 

203-318 
feet  6|  inches  nearly. 

4.  A  rectangular  piece  of  cast  iron,  20  inches  long 
and  6  inches  broad,  is  to  be  formed  of  sufficient  dimen- 
sions to  weigh  150  Ibs. ;   what  will  be  the  depth  re- 
quired ? 

20x6x-263   (see  Table    of   Decimal  Approximations.  Cast 

150 
Iron,  p.  25)  ==  31-96,  and =3  4-69  in.,  or  4  and  11.  in.,  th* 

thickness  required 


38  MENSURATION. 

To  find  the  convex  surface,  and  solidity  or  capacity,  of 
a  cylinder. 

Rule  1.  —  Multiply  the  circumference  of  the  cylinder 
by  its  length  or  height  ;  the  product  is  the  convex  sur- 
face. 

Rule  2.  —  Multiply  the  area  of  the  diameter  by  the 
length  or  height,  and  the  product  is  the  cylinder's  solid- 
ity or  capacity,  as  may  be  required. 

•Application  of  the  Rules. 

1.  The  circumference  of  a  cylinder  is  37£  inches, 
and  its  length  541  inches  ;  required  the  convex  surface 
m  square  feet. 

64-75  X  37-5  X  -007  (see  Table  of  Approximations)  =  14-371 
square  feet. 

2.  A  cylindrical  piece  of  timber  is  9  inches  diameter, 
and  3  feet  4  inches  in  length;  required  its  solidity  in 
cubic  inches,  and  also  in  cubic  feet 

3  feet  4  inches  =  40  inches,  and  92  x-7854  X  40  =  2544-696  cubic 

inches  ;  then  2544-61)6  x  -00058  =  1-4759  cubic  feet. 
.  Suppose  a  well  to  be  4  feet  9  inches  diameter,  and 
16^  feet  from  the  bottom  to  the  surface  of  the  water- 
now  many  imperial  gallons  are  therein  contained  ? 

4-752  x  16-5  x  4-895=  1822-162  gallons. 

4.  Again,  suppose  the  well's  diameter  the  same,  and 
its  entire  depth  35  feet  ;  required  the  quantity  in  cubic 
yards  of  material  excavated  in  its  formation. 

4-7.52  x  35  x  -02909  =  22-973  cubic  yards. 

5.  I  have  a  cylindrical  cistern  capable  of  holding 
7(K)8  gallons,  and  its  depth  is  10  feet;  now  I  want  to 
replace  it  with  one  of  an  equal  depth,  but  capable  of 
holding  12,500  gallons;  what  must  be  its  diameter? 


1  2.500 
4-895  X  10  =  48-95,  and  -^  =  V  255-3  =  15-9687  feet,  or 

15  feet  11$  inches. 
6.  A  cylindrical  piece  of  lead  is  required,  7&  inche* 


MENSURATION.  39 

diameter,  ».nd  168  Ibs,  in  weight;  what  must  be  its 
length  in  inches? 

T5*  x  '3223  =  18,  and  —  =  9-3  inches. 
18 

To  find  the  length  of  a  cylindrical  helix,  or  spiral, 
wound  round  a  cylinder. 

Rule.  —  Multiply  the  circumference  of  the  base  by 
the  number  of  revolutions  of  the  spiral,  and  to  the 
square  of  the  product  add  the  square  of  the  height ;  the 
square  root  of  the  sum  is  the  length  of  the  spiral. 

Application  of  the  Rule. 

L  Required  the  length  of  the  thread  or  screw  twist- 
ing round  a  cylinder  22  inches  in  circumference  3£ 
times,  and  extending  along  the  axis  l(j  inches. 

22  X  3-5  =  772  =  5929,  and  16«  =  256,  then  V  5929  +  256 
=  78-64-  inches. 

2.  The  well  of  a  winding  staircase  is  5  feet  diameter, 
and  height  to  the  top  landing  25  feet ;  the  hand-rail  is 
to  make  2^  revolutions ;  required  its  length. 

5  feet  diameter  =  15-7  feet  circumference. 
15-7  x  2-5  =  S9-252  =  1540-5625,  and  252  =  625,  then 

V1540  +  625  =  46-5  feet,  the  length  required. 

To  find  the  convex  surface,  solidity,  or  capacity  of  a 
cone  or  pyramid. 

Rule  1.  —  Multiply  the  circumference  of  the  base  by 
the  slant  height,  and  half  the  product  is  the  slant  sur- 
face. 

Rule  2.  —  Multiply  the  area  of  the  base  by  the  per- 
pendicular height,  and  one  third  of  the  product  is  the 
solidity  or  capacity,  as  may  be  required. 

Application  of  the  Rules. 

1.  Required  the  area,  in  square  inches,  of  the  slan 
surface  of  a  cone  whose  slant  height  equal  18|  inches, 
and  diameter  at  the  base  6£  inches. 

6*25  X  3-1416  =  19-635  circumference  of  the  base  5  and 

=184.0*1125  square  inches.     ' 
4* 


40 


MENSURATION. 


2.  Required  the  quantity  of  lead,  in  square  feet 
sufficient  to  cover  the  slant  surface  of  a  hexagonal  pyr 
amid  whose  slant  height  is  42  feet,  and  the  breadth  of 
each  side  at  the  base  4  feet  9  inches. 


4-75  X  42  X  6  sides 


=  598-5  square  feet. 


3.  What  is  the  solidity  of  a  cone,  in  cubic  inches,  the 
diameter  at  the  base  being  15  inches,  and  perpendiculai 
height  32£  inches  ? 

152  x  -7854  x  32-5 


3 


-  =1914-4125  cubic  inches. 


4.  In  a  square  solid  pyramid  of  stone  67  feet  in 

height,  and  l(Ji  feet  at  the  base,  how  many  cubic  feet  ? 

16-5  x  16-5  x  67 


To  find  the  solidity  or  capacity  of  any  frustum  &f  a 
wne  or  pyramid. 

Rule.  —  If  the  base  be  a  circle,  add  into  one  sum  the 
two  diameters,  or,  if  a  regular  polygon,  the  breadth  of 
one  side  at  the  top  and  at  the  base;  then  from  the 
square  of  the  sum  subtract  the  product  of  these  di- 
ameters or  breadths  ;  multiply  the  remainder  by  -7854, 
if  a  circle,  or  by  the  tabular  area  (see  Table  of  Poly- 
gons, p.  31)  and  by  one  third  of  the  height;  and  the 
product  is  the  content  in  equal  terms  of  unity. 

Note.  —  Where  the  whole  height  of  the  cone  or  pyramid  can 
be  obtained,  of  which  the  given  frustum  forms  a  part,  the  most 
simple  method  is,  first  to  find  the  whole  contents,  then  the 
contents  extending  beyond  the  fmstum  ;  and,  subtracting  the 
less  from  the  greater,  leaves  the  contents  of 
the  frustum  required. 

•Application  of  the  Rides. 
1.  The  perpendicular  height  A  B 
of  the  frustum  of  a  hexagonal  pyra- 
mid C  D  E,  is  7£  feet,  and  the  breadth 
of  each  side  at  top  and  base  equal 
33  and  %&  feet;  required  the  solid 
contents  of  the  frustum  in  cubic 
feet 


MLNSTJ  RATION. 


41 


5-75  +  2-5  =  6-25,  and  6-25  x  6-25  =  39-0625,  then  3-75  x  2-5  =s 
9-375,  and  39-0625  — 9-375  =  29-6875  x  2-598  (tabular  area,  p 
31)  =  77-138  x  2-5  or  £  of  the  height  =  192-845  cubic  feet. 

2.  Required  the  solidity  of  the  frustum  of  a  cone, 
the  top  diameter  of  which  is  7  inches,  the  base  diametef 
9£,  and  the  perpendicular  height  12. 

7  +  9-52  =  272-25,  and  7x9-5  =  66-5,  then  272-25  —  66-5  = 
205-75  x  -7854  =  161-576  X  4  or  |  of  the  height  =  646-3  cubic 
inches. 

3.  A  vessel  in  the  form  of  an  in-  D 
verted  cone,  as  A  B  C  D,  is  5  feet  in 
diameter  at  the  top,  4   feet  at  the 
bottom,   and   6    feet    in   depth;    re- 
quired its  capacity  in  imperial   gal- 
lons. 


92  =  81,  and  5x4  =  20,  hence  81— 20  =  61  X -7854; 
and  by  2  or  |  of  the  depth  =  95-8188  cubic  feet,  and  X  6-232 
=  597-1427  gallons. 

To  find  the  solid  contents  of  a  wedge. 

Rule.  —  To  twice  the  length  of  the  base  add  tne 
length  of  the  edge ;  multiply  the  sum  by  the  breadth 
of  the  base,  and  by  the  perpendicular  height  from  the 
base,  and  one  sixth  of  the  product  is  the  solid  contents. 

Application  of  the  Rule. 

Required  the  solidity  of  a  wedge,  in 
cubic  inches,  the  base  A  B  C  D  being  9 
inches  by  3£,  the  edge  E  F  7  inches, 
and  the  perpendicular  height  G  E  15. 


-  +  7x3-5x  15_ 


=  218-75  cubic  inches. 


v         11 

To  find  the  convex  surface^  the  solidity,  or  the  capacity, 
a/"  a  sphere  or  globe. 

Rule  1.  —  Multiply  tho  square  of  the  diameter  by 
3'1416 ;  the  product  is  the  convex  surface. 

Rule  2. —  Multiply  the  cube  of  the  diameter  bj 
5236 ;  the  product  is  the  solid  contents. 


42  MENSURATION. 

Rdt  3.  —  Multiply  the  cube  of  the  diametei  *n  feet 
by  3-263,  or  in  inches  by  -001888 ;  the  produce  is  thp 
capacity  in  imperial  gallons.. 

• 

Application  of  the  Rules. 

1.  Required  the  convex  surface,  the  solidity,  and  the 
weight  in  cast  iron  of  a  sphere  or  ball  10£  inches  in 
diameter. 

10-52  x  3-1416  =  346-3t>14  square  inches. 

10-53  X  '5236  =  f>OG- 132.  &c.,  cubic  inches;  and 

606-132  X  -263  (see  Table  of  Approximations,  p.  25)  =  1594  Ibs. 

2.  A  hollow  or  concave  copper  ball  is  required,  8 
inches  diameter,  and  in  weight  just  sufficient  to  sink  to 
its  centre  in  common  water ;  what  is  the  proper  thick 
aess  of  copper  of  which  it  must  be  made  ? 

Weight  of  a  cubic  inch  of  water  =  -03617  Ibs.  )  g« 

«  "  copper  =  -3225      "    $ 

83  x  -5236  X  -03617  _  4.84S2g  cub  ifl  Qf  waler  tQ  be  displaced4 

2 

4-848G)8 
And —=.  15-0334  cubic  inches  of  copper  in  the  ball. 

•3225 

Then  82  x  3-1416  =  201-0624.  and  — =  -0747  inches,  the 

201-0624 

thickness  of  copper  required. 
•0747  x  16  =  Y*£  of  an  inch  full,  or  3  Ibs.  copper  to  a  square  foot. 

3.  What  diameter  must  1  make  a  leaden  ball,  so  ai 
to  weigh  72  Ibs.  ? 

72 

•5236  x  -4103  .-=  -21483308.  and  =  3  V  340  =  6-97 

•21453308 
inches,  diameter. 


INSTRUMENTAL  ARITHMETIC 


UTILITY  OF  THE  SLIDE  RULE. 

THE  slide  rule  is  an  instrument  by  which  the  greatei 
portion  of  operations  in  arithmetic  and  mensuration  may 
be  advantageously  performed,  provided  the  lines  of 
division  arid  gauge  points  be  made  properly  correct, 
and  their  several  values  familiarly  understood. 

The  lines  of  division  are  distinguished  by  the  letters 
A  B  C  D ;  A  B  and  C  being  each  divided  alike,  and 
containing  what  is  termed  a  double  radius,  or  double 
series  of  logarithmic  numbers,  each  series  being  sup- 
posed to  be  divided  into  1000  equal  parts,  and  distrib- 
uted along  the  radius  in  the  following  manner :  — 

From  1  to  2  contains  301  of  those  parts,  being  the  log.  of  2. 

3  "  477  «  3. 

4  "  602  "  4. 

5  "  699  "  5. 

6  "  778  "  6. 

7  "  845  "  7. 

8  «  903  "  8. 

9  "  9.54  "  9 

1000  being  the  whole  number. 

The  line  D,  on  tbe  improved  rules,  consists  of  only  9 
single  radius ;  and  although  of  larger  radius,  the  loga 
rithrnic  series  is  the  same,  and  disposed  of  along  the 
line  in  a  similar  proportion,  forming  exactly  a  line  of 
square  roots  to  the  numbers  on  the  lines  B  C. 


44  INSTRUMENTAL   ARITHMETIC. 


NUMERATION. 

Numeration  teaches  us  to  estimate  or  properly  value 
the  numbers  and  divisions  on  the  rule  in  an  arithmeti- 
cal form. 

Their  values  are  all  entirely  governed  by  the  value 
set  upon  the  first  figure,  and,  being  decimally  reckoned, 
advance  tenfold  from  the  commencement  to  the  termi- 
nation of  each  radius :  thus,  sup'pose  1  at  the  joint  be 
one,  the  I  in  the  middle  of  the  rule  is  ten,  and  1  at  the 
end  one  hundred :  again,  suppose  1  at  the  joint  ten,  1 
in  the  middle  is  100,  and  1  or  10  at  the  end  is  1000, 
&c.,  the  intermediate  divisions  on  which  complete  the 
whole  system  of  its  notation. 


TO    MULTIPLY    NUMBERS    BY    THE    RULE. 

Set  1  on  B  opposite  to  the  multiplier  on  A;  and 
against  the  number  to  be  multiplied  on  B  is  the  prod- 
uct on  A. 

Multiply  6  by  4. 

Set  I  on  B  to  4  on  A  ;  and  against  6  on  B  is  24  on  A.  The 
slide  thus  set,  against  7  on  B  is  28  on  A. 

8  "      3U2    " 

9  "      36    " 
10       «      40    " 
1°2       "      48    « 
15       "      60    " 

25       "     100,  &c  &c. 


TO    DIVIDE    NUMBERS    UPON    THE    RULE. 

Set  the  divisor  on  B  to  1  on  A;  and  against  the 
number  to  be  divided  on  B  is  the  quotient  on  A. 
Divide  63  by  3. 

Set  3  on  B  to  1  on  A ;  and  against  63  on  B  is  21  on  A 


INSTRUMENTAL   ARITHMETIC.  45 


PROPORTION,  OR    RULE    OF    THREE    DIRECT. 

Rule.  —  Set  the  first  term  on  B  to  the  second  on  A 
and  against  the  third  upon  B  is  the  fourth  upon  A. 

1.  If  4  yards  of  cloth  cost  38  shillings,  what  will  3c 
yards  cost  at  the  same  rate  ? 

Set  4  on  B  to  38  on  A  5  and  against  30  on  B  is  285  shillings  on  A, 

2.  Suppose  I  pay  31s.  6d.  for  3  cwt.  of  iron,  at  what 
rate  is  that  per  ton  ?   1  ton  =  20  cwt. 

Set  3  upon  B  to  31-5  upon  A  j  and  against  20  upon  B  i 
upon  A. 


RULE    OF    THREE    INVERSE. 

Rule.  —  Invert  the  slide,  and  the  operation  is  tt** 
same  as  direct  proportion. 

1.  I  know  that  six  men  are  capable  of  performing  t 
certain  given  portion  of  work  in  eight  days,  but  I  wai.l 
the  same  performed  in  three ;  how  many  men  must 
there  be  employed  ? 

Set  6  upon  C  to  8  upon  A  ;  and  against  3  upon  C  is  16  upon  A. 

2.  The  lever  of  a  safety  valve  is  20  inches  in  length, 
and  5   inches  between   the    fixed  end  and  centre   of 
the  valve ;  what  weight  must  tht? re  be  placed  on  the 
end  of  the  lever  to  equipoise  a  force  or  pressure  of  4C 
Ibs.  tending  to  raise  the  valve  ? 

Set  5  upon  C  to  40  upon  A ;  and  against  20  on  C  is  10  on  A. 

3.  If  8|  yards  of  cloth,  \\  yards  in  width,  be  a  suf 
ficient  quantity,  now  much  will  be   required   of  thaj 
which  is  only  £ths  in  width,  to  effect  the  same  purpose  : 

Set  1-5  on  C  to  8-75  on  A  5  and  against  -875  upon  C  is  15  yardt 
upon  A. 


46  INSTRUMENTAL     ARITHMETIC. 


SQUARE     ALND    CUBE    ROOTS    OF    NUMBERS. 

On  the  engineer's  rule,  when  the  lines  C  and  0  are 
equal  at  both  ends,  C  is  a  table  of  squares,  and  D  a 
table  of  roots,  as  — 

Squares,  1     4    9     16    23    36    49    64    81  on  C. 
Roots,      123      4      5      6      7      8      9onD. 

To  find  the  geometrical  mean  proportion  between  tii'O 
numbers, 

Set  one  of  the  numbers  upon  C  to  the  same  number 
upon  D ;  and  against  the  other  number  upon  C  is  the 
mean  number  or  side  of  an  equal  square  upon  L). 

Required  the  mean  proportion  between  20  and  45. 

Set  20  upon  C  to  20  upon  D ;  and  against  45  upon  C  is  30  on 
D. 

To  cube  any  number,  set  the  number  upon  C  to  1  or 
10  upon  D ;  and  against  the  same  number  upon  D  is 
the  cube  number  upon  C. 

Required  the  cube  of  4. 

Set  4  upon  C  to  1  or  10  upon  D ;  and  against  4  upon  D  is  64 
upon  C. 

To  extract  the  cube  root  of  any  number,  invert  the 
slide,  and  set  the  number  upon  B  to  1  or  10  upon  D; 
and  where  two  numbers  of  equal  value  coincide,  on  the 
lines  B  D,  is  the  root  of  the  given  number. 

Required  the  cube  root  of  64. 

Set  64  upon  B  to  1  or  10  upon  D  ;  and  against  *  upon  B  is  \ 
upon  D,  or  root  of  the  given  number. 

On  the  common  rule,  when  1  in  the  middle  of  the 
line  C  is  set  opposite  to  10  on  D,  then  C  is  a  table  of 
squares,  and  D  a  table  of  roots. 

To  cube  any  number  by  this  rule,  set  the  number 
upon  C  to  10  upon  D ;  and  against  the  same  number 
upon  D  is  th-3  cube  upon  C. 


INSTRUMENTAL    MENSURATION.  47 


MENSURATION    OF    SURFACE. 

1.  Squares,  Rectangles ',  fyc. 

Ride.  —  When  the  length  is  given  in  feet  and  the 
Dreadth  in  inches,  set  the  breadth  on  B  to  12  on  A  ;  and 
against  the  length  on  A  is  the  content  in  square  feet  on  B. 

If  the  dimensions  are  all  inches,  set  the  breadth  on 
B  to  144  upon  A ;  and  against  the  length  upon  A  ia 
the  number  of  square  feet  on  B. 

Required  the  content  of  a  board  15  inches  broad  and 
14  feet  long. 

Set  15  upon  B  to  12  upon  A  j  arid  against  14  upon  A  is  17-i 
square  feet  on  B. 

2.  Circles,  Polygons,  Sfc. 

Rule.  —  Set  -7854  upon  C  to  1  or  10  upon  D ;  then 
will  the  lines  C  and  D  be  a  table  of  areas  and  diameters. 

Areas,  3-14  7-06  12-56  19-63  28-27  33-48  50-26  63-61   upon   C. 
Diam.,  234567         8          9        upon  D 

In  the  common  rule,  set  -7854  on  C  to  10  on  D ;  then 
C  is  a  line  or  table  of  areas,  and  D  of  diameters,  as  be 
fore. 

Set  7  upon  B  to  22  upon  A  ;  then  B  and  A  form  or 
become  a  table  of  diameters  and  circumferences  of  cir- 
cles. 

Cir.,  3-14  6-28  9-42   12-56   15-7   18-85  22  25-13  28-27  upon  A 
Dia.,  123         4         56         78         9       upon  B 

Polygons  from  3  to  12  sides.  —  Set  the  gauge-poin 
upon  C  to  1  or  10  upon  D ;  and  against  the  length  o* 
one  side  upon  D  is  the  area  upon  C. 

Sides,  356789        10       11      12. 

Gauge-points,  -433     1-7    2-6  3-63  4-82  6-18    7-69    9-37  11-17 

Required  the  area  of  an  equilateral  triangle,  each 
side  12  inches  in  length. 

Set  -433  upon  C  to  1  upon  D  j  and  against  12  upon  D  are 
62-5  square  inches  upon  C, 

5 


48 


INSTRUMENTAL    MENSURATION. 


TABLE    OF    GAUGE-POINTS    FOR   THE    ENGINEER'S    RULE. 


Names. 

P,  F,P. 

PI  i,  i. 

i,M. 

r.i. 

i,  i. 

p. 

i.  ' 

Cubic  inches 
Cubic  feet 
Imp.  gallons 
Water  in  Ibs. 

578 
1 
163 
16 

83 
144 

231 

23 

1728 

277 
276 

106 
1833 
294 

293 

1273 
22 
353 
352 

105 
121 

306 
305 

121 

33 

529 
528 

Gold     " 

814 

1175 

141 

149 

178 

155 

269 

Silver    " 
Mercury  " 
Brass     « 
Copper   " 

15 
118 
193 
18 

216 
169 
177 
26 

261 
203 
333 
319 

276 
•216 
354 
331 

334 
258 
424 
397 

286 

225 
369 
345 

5 

389 
637 
596 

Lead     " 
Wro'tiron  " 
Cast  iron  " 

141 

207 

222 

203 
297 
32 

243 
357 
384 

258 
338 
407 

31 

453 

489 

27 
394 
424 

465 
682 
733 

Tin      « 

219 

315 

378 

401 

481 

419 

728 

Steel     " 

202 

292 

352 

372 

448 

385 

671 

Coal     " 
Marble   " 
Freestone  " 

127 
591 

632 

183 
85 
915 

22 
102 
11 

33 
116 

1162 

28 
13 
14 

242 
113 
141 

42 
195 
21 

FOR   THq    COMMON    SLIDE    RULE. 

Namea. 

P,  P,P 

P,  i,  i. 

I,  i,  i. 

P,  i. 

I,  i. 

F. 

I. 

Cubic  inches 
Cubic  feet 
Water  in  Ibs. 

36 
625 
10 

518 
9 
144 

624 
108 
174 

6e>o 

114 
184 

799 
138 

22 

625 
119 
191 

113 

206 

329 

Gold            « 
Silver          " 
Mercury     " 
Brass           " 
Copper        " 

507 
938 
738 
12 
112 

735 
136 
122 
174 
163 

88 
157 

127 
207 
196 

96 
173 

132 

221 
207 

118 

2(18 
162 
263 
247 

939 
173 
141 
23 
214 

180 
354 

242 
397 
371 

Lead            " 
Wro't  [ron  " 
Cast  iron    " 

880 
129 
139 

126 

186 

2 

152 

222 
241 

162 
2:35 

254 

194 
283 
304 

lfi<) 
247 
265 

289 
423 
458 

Tin              " 

137 

135 

235 

25 

300 

261 

454 

Steel           " 

136 

183 

22 

tf33 

278 

239 

418 

Coal            " 
Marble        " 
Freestone   " 

795 
370 
394 

114 
53 
57 

138 
637 
69 

146 

725 

728 

116 

81 
873 

151 
72 
755 

262 
121 
132 

INSTRUMENTAL     MENSURATION.  49 


MENSURATION    OF    SOLIDITY    AND    CAPACITY. 

General  rule.  —  Set  the  length  upon  B  to  the  gauge- 
fv  nt  upon  A  ;  and  against  the  side  of  the  square,  or 
a  nneter  on  D,  are  the  cubic  contents,  or  weight  in  Ibs. 
o'  C. 

1.  Required  the  cubic  contents  of  a  tree  30  feet  in 
length,  and  10  inches  quarter  girt. 

Set  20  upon  B  to  144  (the  gauge-point)  upon  A  j  and  against 
10  upon  D  is  20-75  feet  upon  C. 

2.  In  a  cylinder  9  inches   in   length  and  7  inches 
diameter,  now  many  cubic  inches  ? 

Set  9  upon  B  to  1273  (the  gauge-point)  upon  A;  and  against 
7  on  D  is  346  inches  on  C. 

3.  What  is  the  weight  of  a  bar  of  cast  iron  3  inches 
square,  and  6  feet  long  ? 

Set  6' upon  B  to  32  (the  gauge-point)  upon  Aj  and  against 
3  upon  D  is  168  Ibs.  upon  C. 

By  the  common  rule. 

4.  Required  the  weight  of  a  cylinder  of  wrought  iron 
10  inches  long,  and  5£  diameter. 

Set  10  upon  B  to  283  (G.  Ft.)  upon  A;  and  against  5£  upon 
D  is  66-65  Ibs.  on  C. 

5.  What  is  the  weight  of  a  dry  rope  25  yards  long, 
and  4  inches  circumference  ? 

Set  25  upon  B  to  47  (G.  Ft.)  upon  A  5  and  against  4  on  D  is 
63-16  Ibs.  on  C. 

6.  What  is  the  weight  of  a  short-linked   chain  3C 
f  ards  in  length,  and  T\ths  of  an  inch  in  diameter  ? 

Set  30  upon  B  to  52  (G.  Ft.)  upon  A  j  and  against  6  on  D  is 
,29  5  Ibs.  on  C. 


50  INSTRUMENTAL    RULES. 

LAND    SURVEYING. 

If  the  dimensions  taken  are  in  chains,  the  gauge* 
point  is  1  or  10 ;  if  in  perches,  160 ;  and  if  in  yards, 
4840. 

Rule,  _  Set  the  length  upon  B  to  the  gauge-point 
on  A  ;  and  against  the  breadth  upon  A  is  the  content  in 
acres  upon  B. 

1.  Required  the  number  of  acres  or  contents  of  a 
field  20  chains  50  links  in  length,  and  4  chains  40  links 
in  breadth. 

Set  20-5  on  B  to  1  on  A  ;  and  against  4-4  on  A  is  9  acres  on  B. 

2.  In  a  piece  of  ground  440  yards  long,  and  44  broad, 
now  many  acres  ? 

Set  440  upon  B  to  4840  on  A  ;  r.nd  against  44  on  A  is  4  acres 
on  B. 

POWER    OF    STEAM-ENGINES. 

Condensing  Engines.  —  Rule.  Set  3-5  on  C  to  10  on 
D ;  then  D  is  a  line  of  diameters  for  cylinders,  and  C 
the  corresponding  number  of  horses'  power  ;  thus, 
H  Pr  3A      456      8    10  12    16    20  25    30   40    60    on   C. 
C.D.  Join.  101  I*  13$  154  17  181  U21£  24  26|  29$  33|  37|  on   D. 

The  same  is  effected  on  the  common  rule  by  setting 
5  on  C  to  12  on  I). 

Non-condensing  Engines.  —  Rule.  Set  the  pressure 
of  steam  in  Ibs.  per  square  inch  on  B  to  4  upon  A ;  and 
against  the  cylinder's  diameter  on  D  is  the  number  of 
horses'  power  upon  C. 

Required  the  power  of  an  engine,  when  the  cylinder 
is  20  inches  diameter  and  steam  30  Ibs.  per  square 
inch. 

Set  30  on  B  to  4  on  A  5  and  against  20  on  D  is  30  horses' 
oower  on  C. 

The  same  is  effected  on  the  common  rule  oy  setting 
the  force  of  the  steam  on  B  to  250  on  A. 


STRENGTH    OF    MATERIALS.  51 


OF    ENGINE    BOILERS. 

How  many  superficial  feet  are  contained  in  a  boiler 
£}  feet  in  length  and  5£  in  width  ? 

Set  1  upon  B  to  23  upon  A ;  and  against  5-5  upon  B  is  126-5 
square  feet  upon  A. 

If  5  square  feet  of  boiler  surface  be  sufficient  for 
each  horse-power,  how  many  horses'  power  of  engine  is 
the  boiler  equal  to  ? 

Set  5  upon  B  to  126-5  upon  A  5  and  against  1  upon  B  is  25'5 
upon  A. 


STRENGTH  OF  MATERIALS. 

MATERIALS  of  construction  are  liable  to  four  different 
kinds  of  strain ;  viz.,  stretching,  crushing,  transverse 
action,  and  torsion  or  twisting :  the  first  of  which  de- 
pends upon  the  body's  tenacity  alone ;  the  second,  on 
its  resistance  to  compression ;  the  third,  on  its  tenacity 
and  compression  combined ;  and  the  fourth,  on  that 
property  by  which  it  opposes  any  acting  force  tending 
to  change  from  a  straight  line,  to  that  of  a  spiral  direc- 
tion, the  fibres  of  which  the  body  is  composed. 

In  bodies,  the  power  of  tenacity  and  resistance  to 
compression,  in  the  direction  of  their  length,  is  as  the 
cross  section  of  their  area  multiplied  by  the  results  ol 
experiments  on  s-milar  bodies,  as  exhibited  in  the  fol- 
lowing table. 

5* 


52 


STRENGTH  OF    MATERIALS. 


Table  shouring  the  Tenacities,  Resistances  to  Compres- 
sion^ and  other  Properties  of  tfie  common  Materials  oj 
Construction. 


Absolute 

Compared  with  Cast  Iron 

Names  of  Bodies. 

Tenacity 
in  Ibs. 

Resistance 
to  compres- 

Its 

Its  exten- 

Its  stiff- 

persq. 

sion   iu  11.8. 

strength 

sibility   a 

ness  is 

inch. 

per  *q.  in. 

Ash   . 

14130 



0-23 

2-6 

0-089 

Beech 

12225 

8548 

0-15 

2-1 

0-073 

Brass 

17968 

10304 

0-435 

0-9 

0-49 

Brick 

275 

562 

— 

— 



Cast  iron  . 

13434 

86397 

1-000 

1-0 

1-000 

I 

Copper  (wrought)     . 
Elm  .... 

33000 
9720 

1033 

0-21 

2-9 

0-073 

Fir,  or  Pine,  white    . 
"          "      red 

12346 
11800 

2028 
5375 

0-23 
0-3 

2-4 

2-4 

0-1 
0-1 

«          «      yellow  . 

11835 

5445 

0-25 

2-9 

0-087 

Granite  (Aberdeen) 

— 

10910 

— 

— 

— 

Gun-metal  (copper  8, 
and  tin  1  ) 

35838 

__ 

0-65 

1-25 

0-535 

Malleable  iron  . 

56000 

— 

1-12 

0-86 

1-3 

Larch        .        .        <., 

12240 

5568 

0-136 

2-3 

0053 

Lead 

1824 

_ 

0-096 

2-5 

0-0385 

Mahogany,  Honduras 

11475 

8000 

0-24 

2-9 

0-487 

Marble 

551 

6060 

_ 

— 

— 

Oak    . 

11880 

9504 

0-25 

2-8 

0-093 

Rope  (1  in.  in  circum.) 

200 

— 

— 

— 

— 

Steel 

128000 

— 

_ 

__ 

—  _ 

Stone,  Bath 

478 

— 

_ 





"       Craigleith 
«      Dundee  . 

772 
2661 

5490 
6630 

— 

— 

— 

!      "      Portland 

857 

3729 

__ 



_ 

Tin  (cast)  . 

4736 

— 

0182 

0-75 

0-25 

Zinc  (sheet) 

9120 

— 

0-365 

0-5 

0-7,; 

STRENGTH   OF   MATERIALS. 


CO  GO  00  ^1  Ci  O"*  CT« 


CO  I  Circum.  of  rope 
1       in  inches. 


i  CO  C*  N-  CO  ^  .91  ^  »       fSS^in^. 


Diameter  of 
chain  in  inches. 


IO  iO  i-*  t-^  )—  ' 


iO 
tO 


Weight  per 
fathom  in  Ibs. 


CO  Oi  ^—  Oi  CK 


Circum.  of  rope 
in  inches. 


Weight  per 
fathom  inTbs. 


Diameter  of 
chain  in  inches. 


Weight  per 
fathom  in  Ibs. 


t3  W  10  I 


5?! 

r  5* 


Note.  —  It  must  be  understood  and  also  borne  in  mind  that, 
in  estimating  the  amount  of  tensile  strain  to  which  a  body  is 
subjected,  the  weight  of  the  body  itself  must  also  be  taken  into 
account ;  for  according  to  its  position  so  may  it  approximate  to 
its  whole  weight,  in  tending  to  produce  extension  within  itself  3 
as  in  the  almost  constant  application  of  ropes  and  chains  to 
great  depths,  considerable  heights,  &c. 


STRENGTH    OF   MATEKLALS. 


Moys  that  are  of  greater  Tenacity  than  the  Sum  of 
their  Constituents,  as  determined  by  the  Experiments 
of  Muschenbroek. 

Swedish  copper  6  pts.,  Malacca  tin  1 ;  tenacity  per  sq.  inch  64,000  Ibs. 


Chili  copper  G  parts,  Malacca  tin  1 ; 
Japan  copper  5  parts,  Banca  tin  1 ; 
Anjilesea  copper  ft  parts,  Cornish  tin  1 ; 
Common  block-tin  4,  lead  1,  zinc  1; 
Malacca  tin  4,  regulus  of  antimony  1 ; 
Block  tin  3,  lead  1 ; 
Block  tin  8,  zinc  Ij 
Lead  1,  zinc  1 ; 


(10,000 
57,000 
4 1 ,000 
13,000 
j  2,000 
10,200 
10,000 
4,500 


RESISTANCE  TO  LATERAL  PRESSURE,  OR  TRANS- 
VERSE ACTION. 

The  strength  of  a  square  or  rectangular  beam  to  re- 
sist lateral  pressure,  acting  in  a  perpendicular  direction 
to  its  length,  is  as  the  breadth  and  square  of  the  depth, 
and  inversely  as  the  length  ;  —  thus,  a  beam  twice  the 
breadth  of  another,  all  other  circumstances  being  alike, 
equal  twice  the  strength  of  the  other;  or  twice  the 
depth,  equal  four  times  the  strength,  and  twice  the 
length,  equal  only  half  the  strength,  &c.,  according  to 
the  rule. 


Table  o, 


le  of  Data,  containing  the  Results  of  Experiments 
t  the  Elasticity  and  Strength  of  various  Species  oj 
Timber,  by  Mr.  Barlow. 


Species  ol 
Timber. 

Value 
of  E. 

Va!ue 
ofS. 

Species  of 
Timber. 

Value 
ofE. 

Value 

ofS. 

Teak     .     .     . 

174-7 

2462 

Kim       .... 

50-64 

1013 

Poona  .     .     . 

122-26 

2221 

Pitch  pine     .     . 

88-68 

1632 

English  Oak  . 

105 

1672 

Red  pine  .    .     . 

133 

1341 

Canadian  do. 

1555 

1766 

JMew  England  fir 

158-5 

1102 

Dantzic     do. 

86-2 

1457 

Riga  fir      ... 

90 

1100 

Adriatic    do. 

70-5 

1383 

Mar  Forest    do. 

63 

1200 

Ash  ... 

119 

2026 

Larch   .... 

76 

900 

Be«ch  .    .    . 

98 

1556 

Norway  spruce  . 

105-47 

1474 

STRENGTH    OF    MATERIALS.  55 

To  find  the  dimensions  of  a  beam  capable  of  sustain" 
ing  a  given  weight,  with  a  given  degree  of  deflection, 
when  supported  at  both  ends. 

Rule.  —  Multiply  the  weight  to  be  supported  in  Ibs. 
by  the  cube  of  the  length  in  feet  ;  divide  the  product 
by  32  times  the  tabular  value  of  E,  multiplied  into  the 
given  deflection  in  inches  ;  and  the  quotient  is  the 
breadth  multiplied  by  the  cube  of  the  depth  in  inches. 

Note  1.  —  When  the  beam  is  intended  to  be  square,  then  the 
fourth  root  of  the  quotient  is  the  breadth  and  depth  required. 

Note  2.  —  If  the  beam  is  to  be  cylindrical,  multiply  the 
quotient  by  1-7,  and  the  fourth  root  of  the  product  is  the  di 
ameter. 

Ex.  The  distance  between  the  supports  of  a  beam  ot 
Riga  fir  is  16  feet,  and  the  weight  it  must  be  capable 
of  sustaining  in  the  middle  of  its  length  is  8000  lbs.; 
with  a  deflection  of  not  more  than  f  of  an  inch  ;  what 
must  be  the  depth  of  the  beam,  supposing  the  breadth 
8  inches  ? 


To  determine  the  absolute  strength,  of  a  rectangular 
beam  of  timber,  when  supported  at  both  ends,  and  loaded 
in  the  middle  of  its  length,  as  beams  in  general  ought  to 
be  :alculated  to,  so  that  they  may  be  rendered  capable  oj 
withstanding  all  accidental  cases  of  emergency. 

Rule.  —  Multiply  the  tabular  value  of  S  by  four 
times  the  depth  of  the  beam  in  inches,  and  by  the  area 
of  the  cross  section  in  inches  ;  divide  the  product  by 
the  distance  between  the  supports  in  inches,  and  the 
quotient  will  be  the  absolute  strength  of  the  beam  in  Ibs. 

./Vote  I.  —  If  the  beam  be  not  laid  horizontally,  the  distance 
between  the  supports,  tor  calculation,  must  be  the  horizontal 


2.— One  fourth  of  the  weight  obtained  by  the  rule,  is 
the  greatest  weight  that  ought  to  be  applied  in  practice  as  per* 
teanent  load. 


06  STRENGTH    OF    MATERIALS. 

Note  3.  —  If  the  load  is  to  be  applied  at  any  other  point  than 
the  middle,  then  the  strength  will  be  as  the  product  ol  the 
two  distances  is  to  the  square  of  half  the  length  of  the  beam 
between  the  supports  ;  —  or,  twice  the  distance  from  one  end, 
multiplied  by  twice  from  the  oilier,  and  divided  by  the  whole 
length,  equal  the  effective  length  of  the  beam. 

Ex.  In  a  building  18  feet  in  width,  an  engine  boiler 
of  5i  tons  is  to  be  fixed,  the  centre  of  which  to  be  7 
feet  from  the  wall  ;  and  having  two  pieces  of  red  pine, 
10  inches  by  (>,  which  1  can  lay  across  the  two  walls 
for  the  purpose  of  slinking  it  at  each  end,  —  may  1 
with  sufficient  confidence  ^apply  them,  so  as  to  effect 
this  object  ? 

2240  x  5-5  __  g  to  carry  at  each  en(j. 


And  18  feet  —  7  =  11,  double  each,  or  14  and  22,  then 
14  *  u~l  -  n  feet,  or  "204  inches,  effective  length  of  beam. 
18 

Tabular  value  of  S,red  pine.  =  '»"  X  \^^=  W™»"- 
the  absolute  strength  of  each  piece  of  timber  at  that  point. 

To  determine  the  dimensions  of  a  rectangular  beam 
capable  of  supporting  a  required  weight,  with  a  given 
degree  of  defection,  when  jixed  at  one  end. 


Rule%  _  Divide  the  weight  to  be  supported,  in  Ibs., 
by  the  tabular  value  of  K,  multiplied  by  the  breadth 
and  deflection,  both  in  inches  ;  and  tfie  cube  root  of  the 
quotient,  multiplied  by  the  length  in  feet,  equal  the 
depth  required  in  inches. 

Ex.  A  beam  of  ash  is  intended  to  bear  a  load  of  700 
Ibs.  at  its  extremity  ;  its  length  being  5  feet,  its  breadth 
4  inches,  and  the  deflection  not  to  exceed  £  of  an  men, 

Tabular  value  ofE  =  1  19  X  4  X  -5  =  238  the  divisor  ; 
then  700-i-  238  —  3  y^-94  x  5  =  7-25  inches,  depth  of  the  beam 


STRENGTH    OF    MATERIALS.  5? 

To  find  the  absolute  strength  of  a  rectangular  learn, 
when  fixed  at  one  end,  and  loaded  at  the  other. 

Rule.  —  Multiply  the  value  of  S  by  the  depth  of  the 
beam,  and  by  tne  area  of  its  section,  both  in  inches ; 
divide  the  product  by  the  leverage  in  inches,  and  the 
quotient  equal  the  absolute  strength  of  the  beam  in  Ibs. 

Ex.  A  beam  of  Riga  fir,  12  inches  by  4£,  and  pro- 
jecting G.i  feet  from  the  wall ;  what  is  the  greatest 
weight  it  will  support  at  the  extremity  of  its  length  ? 

Tabular  value  of  S  =  1 100 
12  x  4-5  =  54  sectional  area, 

Then,  110°  x  12><54  =  9133.4  Ibs. 

When  fracture  of  a  beam  is  produced  by  vertical 
pressure,  the  fibres  of  the  lower  section  of  fracture  are 
separated  by  extension,  whilst  at  the  same  time  those 
of  the  upper  portion  are  destroyed  by  compression 
hence  exists  a  point  in  section  where  neither  the  one 
nor  the  other  takes  place,  and  which  is  distinguished  as 
the  point  of  neutral  axis.  Therefore,  by  the  law  of 
fracture  thus  established,  and  proper  data  of  tenacity 
and  compression  given,  as  in  the  table,  (p.  52)  we  are 
enabled  to  form  metal  beams  of  strongest  section  with 
the  least  possible  material.  Thus,  in  cast  iron,  the  resis- 
tance to  compression  is  nearly  as  fi£  to  1  of  tenacity ; 
consequently  a  beam  of  cast  iron,  to  be  of  strongest 
j-^-3  section,  must  be  of  the  following  form, 

and  a  parabola  in  the  direction  of  its 
length,  the  quantity  of  material  in  the 
|  v  \  bottom  flange  be  ng  about  6^  times  that 
of  the  upper.  But  such  is  not  the  case  with  beams  oi 
timber ;  for  although  the  tenacity  of  timber  be  on  an 
average  twice  that  of  its  resistance  to  compression,  its 
flexibility  is  so  great,  that  any  considerable  length  of 
beam,  where  coiumns  cannot  be  situated  to  its  support, 


58 


STRENGTH    OF    MATERIALS. 


requires  to  be  strengthened  or  trussed  by  iron  rods,  a* 
in  the  following  manner. 


And  these  applications  of  principle  not  only  tend  to 
diminish  deflection,  but  the  required  purpose  is  also 
i/iore  effectively  attained,  and  that  by  lighter  pieces  oi 
timber. 

To  ascertain  the  absolute  strength  of  a  cast  iron  beam 
of  the  preceding  J brm,  or  that  of  strongest  section. 

Rule.  —  Multiply  the  sectional  area  of  the  bottom 
flange  in  inches  by  the  depth^  of  the  beam  in  inches, 
and  divide  the  product  by  the  distance  between  the 
supports,  also  in  inches ;  and  514  times  the  quotient 
equal  the  absolute  strength  of  the  beam  in  cwts. 

The  strongest  form  in  which  any  given  quantity  of 
matter  can  be  disposed  is  that  of  a  hollow  cylinder ;  and 
it  has  been  demonstrated  that  the  maximum  of  strength 
is  obtained  in  cast  iron,  when  the  thickness  of  the  an- 
nulus,  or  ring,  amounts  to  ith  of  the  cylinder's  external 
diamete~ ;  the  relative  strength  of  a  solid  to  that  of  a 
hollow  cylinder  being  as  the  diameters  of  their  sec- 
tions. 


STRENGTH    OF  MATERIALS. 


59 


•#  Table  showing  the  Weight  or  Pressure  a  Beam  of 
Cast  Iron,  ]  inch  in  breadth,  ivill  sustain,  without  de- 
stroying its  elastic  force,  when  it  is  supported  at  each 
end,  and  loaded  in  the  middle  of  its  length,  and  also  tht 
defection  in  the  middle  which  that  weight  will  produce 
By  Mr.  Hodgkinson,  Manchester. 


Length. 

6  feet. 

7  feet. 

8  feet. 

9  feet. 

10  feet. 

Depth 

Wt.  in 

Defl. 

Wt.in 

De8. 

Wt.in    Defl. 

Wt.      Defl. 

Wt.  in 

Defl. 

in  in. 

Ibs. 

in  in. 

Ibs. 

in  in. 

Iba. 

in  m. 

in   Ibs. 

in  in. 

Ibs. 

3 

4~ 

1278 
1739 
2272 

•24 

•205 
•18 

1089 
1482 
1936 

•33 

•28 
•£45 

954 
1298 
1700 

•426 
•365 
•32 

855  -54 
1164)  '46 
15201  -405 

765 
1041 
1360 

•66 

:f 

44 

2875 

•16 

2450 

•217 

2146 

•284 

19241-36 

1721 

•443 

5  ' 

3560 

•144 

3050 

•196 

2650 

•256 

2375  -32 

2125 

•4 

6 

5112 

•12 

4356 

•163 

3816 

•213 

3420!  -27 

30601  -33 

7 

6958 

•103 

5929 

•14 

5194J  -183 

4655  -23 

41651  -29 

8 

9088 

•09 

7744 

•123 

6784 

•16 

6080 

•203 

5440!  -25 

9 

'  — 

— 

9801 

•109 

8586 

•142 

7695 

•18      6885  -22 

10 

— 

— 

12100 

•098 

10600  -128 

9500 

•162   8500 

•2 

11 









12826  -117 

11495 

•15  110285 

•182 

12 

— 

— 

— 

— 

15264  -107 

13C80 

•135  12240 

17 

13 

— 

— 

— 







16100 

•125  14400 

•154 

14 

— 

— 

— 

— 

— 

— 

18600  -115 

16700 

•143 

12  feet. 

14  feet. 

16  feet. 

18  fret. 

20  fert. 

6 

2548,  -48 

2184 

•65 

1912 

•85 

1699  1-08 

1530  1-34 

7 

34711  -41 

2975 

•58 

2603 

•73 

2314    -93 

2D82  1-14 

8 

4532!  -36 

3884 

•49 

3396 

•64 

302) 

*81 

2720  H)0 

9 

5733  -32 

4914 

•44 

4302 

•57 

3825 

•72 

34381  -89 

10 

7083;  -28 

6071 

•39 

53121  -51 

4722 

•64 

4250J  -8 

11 

8570  -26 

7346 

•36 

64281  -47 

5714 

•59 

5142J  -73 

12 

10192  -24 

8736 

•a3     7648!  -43 

6796 

•54 

6120!   -67 

13 

11971-22    10260 

•31      8978  -39 

7980 

•49 

7182    -61 

14 

13883!  -21    11900 

•28    10412 

•36 

9255 

•46 

8330 

•57 

15 

15937  -19    13660 

•26    11952 

34 

10624 

•43 

9562 

•53 

16 

18128  -18  ;  15536 

•24 

13584 

•32 

12080 

•40 

10880J  -5 

17 

20500:  -17  i  17500 

•23    15353  -3    1  13647 

•38 

12282 

•47 

18 

229321  -16  19656 

•21   !  17208!  -28    15700 

•36 

13752    -44 

Note.  —  This  Table   shows   the  greatest  weight  that   eve* 
ought  to  be  laid  upon  a  beam  for  permanent  load  ;  and,  if  therfl 
be  any  liability  to  jerks,  &c.,  ample  allowance  must  be  made 
ulso,  the  weight  of  the  beam  itself  must  be  included 

6 


CO  STEENtTH    OF    MATERIALS. 

To  find  the  weight  of  a  cast  iron  beam  of  given  dinien- 
9ions. 

Rule.  —  Multiply  the  sectional  area  in  inches  by  the 
length  in  feet,  and  by  3-^,  the  product  equal  the  weight 
in  Ibs. 

Ex.  Required  the  weight  of  a  uniform  rectangular 
beam  of  cast  iron,  1<>  feet  in  length,  11  inches  in 
breadth,  and  1£  inch  in  thickness. 

11  X  1-5  X  16  X  3-°2  =  844-8  Ibs. 

Resistance  of  Bodies  to  Flexure  by  vertical  Pressure. 

When  a  piece  of  timber  is  employed  as  a  column  or 
support,  its  tendency  to  yielding  by  compression  is  dif- 
ferent according  to  the  proportion  between  its  length 
and  area  of  its  cross  section ;  and  supposing  the  form 
that  of  a  cylinder  whose  length  is  less  than  seven  or 
eight  times  its  diameter,  it  is  impossible  to  bend  it  by 
any  force  applied  longitudinally,  as  it  will  be  destroyed 
by  splitting  before  that  bending  can  take  place;  but 
when  the  length  exceeds  this,  the  column  will  bend 
under  a  certain  load,  and  be  ultimately  destroyed  by 
a  similar  kind  of  action  to  that  which  has  place  in  the 
transverse  strain. 

Columns  of  cast  iron  and  of  other  bodies  are  also 
similarly  circumstanced,  this  law  having  recently  been 
fully  developed  by  the  experiments  of  Sir.  Hodgkinson 
on  columns  of  different  diameters,  and  of  different 
lengths. 

When  the  length  of  a  cast  iron  column  with  flat 
ends  equals  about  thirty  times  its  diameter,  fracture 
will  be  produced  wholly  by  bending  of  the  material. 
When  of  less  length,  fracture  takes  place  partly  by 
crushing  and  partly  by  bending.  But,  when  the  column  • 
is  enlarged  in  the  middle  of  its  length  from  one  and  a 
half  to  twice  its  diameter  at  the  ends,  by  being  cast  hol- 
low, the  strength  is  greater  by  ith  than  in  a  solid  columi 
Containing  the  same  quantity  of  material. 


STRENGTH    OF    MATERIALS.  61 


To  determine  the  dimtiisions  of  a  support  or  column  to 
Jew,  without  sensible  curvature,  a  given  pressure  in  tht 
direction  of  its  axis. 

Rule.  —  Multiply  the  pressure  to  be  supported  in  Ibs. 
by  the  square  of  the  column's  length  in  feet,  and  divide 
the  product  by  twenty  times  the  tabular  value  of  E  ;  and 
the  quotient  will  be  equal  to  the  breadth  multiplied  by 
the  cube  of  the  least  thickness,  both  being  expressed  in 
inches. 

Note  1.  —  When  the  pillar  or  support  is  a  square,  its  side 
will  be  the  fourth  root  of  the  quotient. 

2.  If  the  pillar  or  column  be  a  cylinder,  multiply  the  tabular 
value  of  E  by  12,  and  the  fourth  root  of  the  quotient  equal  the 
diameter. 

Ex.  1.  What  should  be  the  least  dimensions  of  an 
oak  support,  to  bear  a  weight  of  2240  Ibs.  without  sensi- 
ble flexure,  its  breadth  being  3  inches,  and  its  length  5 
feet? 

Tabular  value  of  E  =  105, 

°><24o  v  52 
and  =  3  V  ««8  =  2-05  inche,. 


Ex.  2.  Required  the  side  of  a  square  piece  of  Riga 
fir,  9  feet  in  length,  to  bear  a  permanent  weight  of 
6000  Ibs. 

Tabular  value  of  E  =  96, 

'iflflO  V  ()2 

and  t-        ^  =  4  V  253  =  4  inches  nearly. 

^.0  X  Jo 


STRENGTH    OF    MATERIALS. 


51 


Si 


| 


CO  3*  sC  "f  r*  OQ  i 

1-1  s*  *o  Oi  "*  o  : 


Ci  ^  "O  Tf  00  Z) 


2S§I2SI%i822ga 

--Sm^-ooog^j-^g 


STRENGTH    OF  MATERIALS.  63 


Practical  Utility  of  the  preceding  Table. 

Ex.  Wanting  to  support  the  front  of  a  building  with 
cast  iron  columns  18  feet  in  length,  8  inches  in  diam- 
eter, and  the  metal  1  inch  in  thickness ;  what  weight 
may  F  confidently  expect  each  column  capable  of  sup- 
porting without  tendency  to  deflection? 

Opposite  8  inches  diameter  and  under  18  feet  =  1097 
Also  opposite  6  in.  diameter  and  under  18  feet=   440 

=   657  cwt. 

Note.  —  The  strength  of  cast  iron  as  a  column  being  1-0000 

steel  "  =2-518 

"  wrought  iron       "  =  1-745 

"  (oak)  Dantzic      «  =    -1088 

«  red  deal  «  =   -0785 


Elasticity  of  Torsion,  or  Resistance  of  Bodies  to 
Twisting. 

The  angle  of  flexure  by  torsion  is  as  the  length  and 
extensibility  of  the  body  directly  and  inversely  as  the 
diameter;  hetice,  the  length  of  a  bar  or  shaft  being 
given,  the  power,  and  the  leverage  the  power  acts  with, 
being  known,  and  also  the  number  of  degrees  of  torsion 
that  will  not  affect  the  action  of  the  machine,  to  deter- 
mine the  diameter  in  cast  iron  with  a  given  angle  of 
flexure. 

Rule.  —  Multiply  the  power  in  Ibs.  by  the  length  of 
the  shaft  in  feet,  and  by  the  leverage  in  feet ;  divide  the 
product  by  fifty-five  times  the  number  of  degrees  in  the 
angle  of  torsion ;  and  the  fourth  root  of  the  quotient 
equal  the  shaft's  diameter  in  inches. 

Ex.  Required  the  diameters  for  a  series  of  shafts  35 
feet  in  length,  and  to  transmit  a  power  equal  to  VM5 
*bs,  acting  at  the  circumference  of  a  wheel  2£  feet 
6* 


64  MECHANICS. 

radius,  so  that  the  twist  of  the  shafts  on  the  application 
of  the  power  may  not  exceed  one  degree. 

1245  X  35  X  2-5 


53x  I 


=  4y  1931  =6-67  inches  in  diameter. 


Relative  Strength  of  Metals  to  resist  Torsion. 
st  iron  ...==!• 


°PP< 

yellow  Brass     .    =    -511 
Gun  metal      .    .    =   -55 


Swedish  bar  iron  .  =  1'05 

English      do.  ,     .  =1-12 

Sheer  steel       .    .  =1-96 

Cast  do.  .    .  =  2-1 


MECHANICS. 

PRELIMINARY    REMARKS. 

MECHANICS,  regarded  as  a  science,  comprehends  the 
sum  of  our  knowledge  relative  to  the  sensible  motions 
of  bodies  either  actually  existing  or  expressed  by  the 
opposition  of  forces  tending  to  produce  motion.  The 
science  is  thus  resolvable  into  a  code  of  discovered  laws, 
applying  to  the  causes  which  occasion  and  modify  the 
direction  and  the  velocities  of  motion,  and  is  therefore 
distinct  from  those  branches  of  science  in  which,  al- 
though presenting  phenomena  of  motion  in  sensible 
portions  of  matter^  we  do  not  consider  the  circumstances 
and  laws  of  these  motions,  but  only  the  effects  pro- 
duced. 

When  motion  itself  is  considered,  the  reasoning  be- 
longs to  mechanics,  and  it  is  probable  that  as  our  knowl- 
edge of  th*»  laws  which  govern  the  phenomena  that  are 


MECHANICS.  65 

evolved  under  the  hand  of  the  experimental  philosopher 
becomes  more  extended,  a  wider  meaning  will-  be  given 
to  the  science  of  motion.  The  definition  which  is  here 
given  of  mechanics  is  not  coeval  with  the  name.  The 
science,  like  most  other  sciences,  has  gradually  ex- 
panded to  its  present  extent.  It  was  originally  the  sci- 
ence of  machines  —  these  being  the  first  subjects  of 
its  speculation ;  and,  as  everv  material  combination  em- 
ployed for  producing  or  preventing  motion  may  be 
regarded  as  a  machine,  and  may  be  resolved  into  the 
same  elementary  principles  as  those  employed  in  ma- 
chines, —  the  mechanical  powers,  —  the  name  "  mechan- 
ics "  became  to  be  applied  to  motion,  the  tendency  to 
motion  of  any  bodies  whatever.  Mechanics  still  con- 
tinues to  be  defined  by  some  the  science  of  force,  and 
there  does  not  appear  to  be  any  valid  objection  to  che 
definition.  Force  is  the  cause  of  motion,  and  its  laws 
are  identical  with  the  laws  of  motion :  and,  consequently, 
the  science  of  force  coincides,  in  all  its  parts,  with  the 
science  of  motion,  which  is  mechanics. 


ELEMENTS  OF   MACHINERY. 


THE    LEVER. 

To  produce  mechanical  effects,  it  is  rarely  conve- 
nient to  apply  directly  our  available  force,  —  mean- 
ing by  mechanical  effect  moving  a  body  of  a  certain 
weight  through  a  certain  space,  —  the  assistance  of  ma- 
chinery is  required.  In  fact,  the  essential  idea  of  ma- 
chinery is,  that  it  renders  force  available  for  effecting 
certain  practical  ends.  Machines  prepare,  as  it  were, 
the  raw  material  of  force  supplied  to  us  from  natural 
sources.  It  is  transmitted  and  modified  by  certain 
combinations  of  the  elements  of  machinery,  and  is 
given  off,  at  last,  in  a  condition  suitable  for  producing  the 


66  MECHANICS. 

desired  mechanical  effect.  We  do  not  create  force 
the  end  of  machinery  is  just  to  transmit  it.  and  diffuse  01 
concentrate  it  m  one  or  more  points  of  action.  The 
various  diffused  or  concentrated  forces,  then,  being 
added  together,  will  just  amount  to  the  original  avail 
able  force. 

All  machinery,  when  analyzed,  will  be  found  to  con- 
sist of  a  combination  of  six  simple  machines,  or  ele- 
ments, commonly  called  mechnnicitl  powers.  This  term 
is  not  correctly  applied  to  these  elements.  They  are 
not  powers,  or,  in  other  words,  sources  of  power  or  fo^e 
they  simply  transmit  and  diffuse  or  concentrate  forces. 
These  six  elements  are,  the  lever,  the  pulley,  the  ivheel 
and  axle,  the  inclined  plane,  the  wedge,  and  the  screw. 

To  understand,  therefore,  the  nature  of  any  machine, 
t  correct  idea  of  these  elements  is  requisite. 

A  lever  is  an  inflexible  rod,  by  the  application  of 
which  one  force  may  balance  or  overcome  another. 
These  forces  are  termed,  respectively,  the  power  and  the 
resistance  or  weight,  not  from  any  difference  in  the  action 
of  the  forces,  but  with  reference  merely  to  the  intention 
with  which  the  machine  is  used ;  and  indeed  the  same 
terms  are  used  about  all  the  other  mechanical  elements. 
In  applying  the  rod  to  operate  upon  any  resistance,  it 
must  rest  upon  a  centre  prop,  or  fulcrum,  somewhere 
along  its  length,  upon  which  it  turns  in  the  performance 
of  its  work.  Thus,  there  are  three  points  in  every  lever, 
to  be  regarded  in  examining  its  action,  namely,  the  two 
points  of  application  of  the  power  and  the  weight,  and 
the  point  resting  on  the  fulcrum.  There  is  a  certain  rela- 
tion to  be  observed  between  the  magnitudes  of  the  op- 
posing force,  and  their  distances  from  the  fulcrum, 
namely,  that,  in  every  case,  the  power,  multiplied  by  its 
distance  from  the  fulcrum,  is  equal  to  the  weight, 
multiplied  by  its  distance  from  the  same  point.  From 
this,  simple  rules  may  be  deduced  for  calculation. 

To  know  the  power  to  be  applied,  at  a  certain  dis- 
tance from  the  fulcrum,  to  overcome  a  resistance  acting 
also  at  a  certain  distance,  multiply  the  resistance  by  its 


MECHANICS, 


67 


distance  from  the  fulcrum,  which  gives  its  moment,  and 
divide  the  product  by  the  distance  given.  Quotient  will 
be  the  power,  it  being  observed  that  the  distance  and 
the  force  be  each  expressed  in  the  same  unit  of  measure. 
For  example,  a  weight,  1120  Ibs.,  at -3  inches  from  the 
fulcrum,  is  to  be  balanced  by  a  force  at  the  distance  of 
10  feet  Now  10  feet  are  equal  to  120  inches ;  and  the 
moment  of  1120  Ibs.  is  1 120  X  3  =  3300.  Divide  this 
by  120,  we  have  28  Ibs.  for  the  power  required. 

Again ;  to  know  the  distance  at  which  a  given  force 
ought  to  be  applied  to  balance  a  given  weight  at  a  certain 
distance,  we  must,  in  like  manner,  multiply  the  weighc 
by  its  distance,  as  before,  and  divide  by  the  given 
power.  1120  Ibs.,  for  example,  at  3  inches  distance, 
are  to  be  balanced  by  a  force  of  28  Ibs.  To  find  the 
distance  of  this  weight,  1120  Ibs.  multiplied  by  3,  give 
3360,  which,  divided  by  28,  give  120  inches,  or  10  feet 


THE    WHEEL    AND    AXLE,   OR    CRANE. 

The  mechanical  advantage  of  the  wheel  and  axle,  or 
crane,  is  as  the  velocity  of  the  weight  to  the  velocity 
of  the  power ;  and,  being  only  a  modification  of  the 
first  kind  of  lever,  it  of  course  partakes  of  the  same 
principles. 

To  determine,  the  amount  of  effective  power  produced 
from  a  given  power,  by  means  of  a  crane  with  known 
peculiarities. 

Rule,.  —  Multiply  together  the  diameter  of  the  circle 
described  by  the  handle  and  the  number  of  revolutions 
of  the  pinion  to  one  of  the  wheel ;  divide  the  product  by 
the  barrel's  diameter  in  equal  terms  of  dimensions  ;  and 
the  quotient  is  the  effective  power  to  1  of  exertive  force. 

Ex.  Let  there  be  a  crane,  the  handle  of  which  de- 
scribes a  circle  of  30  inches  in  diameter;  the  pinion 
makes  8  revolutions  for  1  of  the  wheel,  and  the  barrel 


68  MECHANICS 

is  11  inches  in  diameter;  required  the  effective  power 
in  principle,  also  the  weight  that  36  Ibs.  would  raise, 
friction  not  taken  into  account 

30X  8  =  21-9  to  1  of  exertive  force,  and  21-9  X  36  =  785-5  Ibs. 
11 

Given  any  two  parts  of  a  crane,  to  find  the  third  that 
sltall  produce  any  required  proportion  of  mechanical  effect. 

Rule.  —  Multiply  the  two  given  parts  together,  and 
the  quotient  is  the  dimensions  of  the  other  parts  in  equal 
terms  of  unity. 

Ex.  Suppose  that  a  crane  is  required,  the  ratio  of 
power  to  effect  being  as  40  to  1,  and  that  a  wheel  and 
pinion  J 1  to  1  is  unavoidably  compelled  to  oe  employed; 
also  the  throw  of  each  handle  to  be  16  inches;  what 
must  be  the  barrel's  diameter,  on  which  the  rope  or 
chain  must  coil  ? 

16x2  =  32  inches  diameter  described  by  the   handle. 
And  32  x  11  =  8-8  inches,  the  barrel's  "diameter. 

40 


THE    PULLEY. 

The  principle  of  the  pulley,  or  more  practically  the 
block  and  tackle,  is  the  distribution  of  weight  on  vari- 
ous points  of  support;  the  mechanical  advantage  derived 
depending  entirely  upon  the  flexibility  and  tension  of 
the  rope,  and  the  number  of  pulleys  or  shelves  in  the 
lower  or  rising  block.  Hence,  by  blocks  and  tackle  of 
the  usual  kind,  the  power  is  to  the  weight  as  the  num- 
ber of  cords  attached  to  the  lower  block ;  whence  the 
following  rules :  — 

1.  Divide  the  weight  to  be  raised  by  the  number  of 
cords  leading  to,  from,  or  attached  to  the  lower  block ; 
and  the  quotient  is  the  power  required  to  produce  ac 
equilibrium,  provided  friction  did  not  exist 

2.  Divide  the  wejgnt  to  be  raised  oy  tne  power  to  be 


MECHANICS.  09 

applied  :  the  quotient  is  the  number  of  shelves  in,  or  cords 
attached  to,  the  rising  block. 

Ex.  Required  the  power  necessary  to  raise  a  weight 
of  3000  Ibs.  by  a  four  and  five  shelved  block  and  tackle, 
the  four  being  the  movable  or  rising  block. 

Necessarily,  there  are  nine  cords  leading  to  and  from 
the  rising  block ;  — 

3000 
Consequently, =  333  lbsv  the  power  required. 

i'l.  2.  I  require  to  raise  a  weight  4256  Ibs.;  the 
amount  of  my  power  to  effect  this  object  being  50Q  Ibs. 
What  kind  of  block  and  tackle  must  1,  of  necessity,  em- 
ploy ? 

425<» 

=  8-51  cords  —  of  necessity,  there  must  be  4  shelves, 

600 

or  9  cords,  in  the  rising  block. 

As  the  effective  power  of  the  crane  may,  by  addi- 
tional wheels  and  pinions,  be  increased  to  any  required 
amount,  so  may  the  pulley  and  tackle  be  similarly  aug- 
mented by  purchase  upon  purchase.  Two  of  the  most 
useful  are  known  by  the  term  runner  and  tackle,  and  the 
second  by  that  of  Spanish  burton. 


70 


THE    INCLINED    PLANE. 


T-<         C:  *>•  'O  lO  "s^  CO  Ctt  -« 
i-ii-iOOOGOOOO 


00000000 
oooooooo 


OOOOO 


OOO 


C£>  S*  C:  ift  C«  00  13  G»  03 

en  i-  x  x  no  t^  t>-  i^  to 


r?  ^  ^?  7J  7i  7J  (>?  ?J  O? 

oooooooooo 
oooooooooo 


"^  O  l> 
13  70  -H 


O 
00  t 

COC 


L.O  ^D 

O  7J 


CiXl»l>sOsCiOOLO 

r-tOOOOOOOOO 

oooooooooo 


> 

lOCOOIdr-ir-(—  <i—  I 
i-»OOOOOOOO 


ooo 
t-KMco 


ooooo 


Note.—* Although  this  table  has  been  calculated  particularly 
for  carriages  on  railway  inclines,  it  may  with  equal  propriety  be 
applied  to  any  other  incline,  the  amount  of  traction  on  a  level 
being  known. 


THE    INQLINED    PLANE.  71 


Application  of  the  preceding  Table. 

1.  What  weight  will  a  tractive  power  of  150  Ibs. 
draw  up  an  incline  of  I   in  340,  the  resistance  on  the 
level    being  estimated  at  z^ffth  part  of  the  insistent 
weigat  ? 

In  a  line  with  40  in  the  left-hand  column  and  unde1* 
200  is     ................     00417 

Also,  in  the  same  line  and  under  300  is   .....     -00294 

Added  together  =  -00711 

150 

Then  -  =  21097  Ibs.  weight  drawn  up  the  plane 
•00711 

2.  What  weight  would  a  force  of  150  Ibs.  c;aw  down 
the  same  plane,  the  friction  on  the  level  be'jif  Jie  same 
as  before  ? 

Friction  on  the  level  .  "00417 
Gravity  of  the  plane    =-  •OOiU-S  subtract 


150 

And  —  -  —  121915  Ibs.  woiff!.'t  dr-.wn  down  the  plane. 
•00123 


Example  of  Incline  wlien  Velocity  is  taken  into  Account. 

A  power  of  230  Ibs.  at  a  velocity  of  75  feet  per  min- 
nte,  is  to  be  enployed  for  moving  weights  up  an  inclined 
plane  14<J  feet  "in  height  and  Hv*  feet  in  length,  the  least 
velocity  of  the  weight  to  oe  8  feet  per  minute  ;  required 
the  greatest  weight  that  the  power  is  equal  to. 


MM,  ,bs  or 

12X8  96 


72  MECHANICS. 


THE    INCLINED    PLANE. 

The  inclined  plane  is  the  representative  of  the  second 
class  of  mechanical  elements.  Its  fundamental  law  of 
action  is  that  of  the  composition  and  resolution  of  forces. 
The  manner  in  which  the  advantage  is  immediately  cie- 
rived  from  it  is,  therefore,  distinct  from  that  of  the  first 
class  ;  there  is  necessarily  a  fulcrum,  a  point  round 
which  all  the  motion  takes  place,  and  through  which 
the  power  acts  on  the  resistance  ;  -whereas,  in  this  class, 
there  is  no  apparent  centre  of  action.  The  advantage 
gained  hy  the  inclined  plane,  when  the  power  acts  in  a 
parallel  direction  to  the  plane,  is  as  the  length  to  the 
height  or  angle  of  inclination.  Hence  the  rule.  Divide 
the  weight  liy  the  ratio  of  inclination,  and  the  quotient 
equal  the  power  that  will  just  support  that  weight  upon 
the  plane.  Or,  multiply  the  weight  by  the  height  of 
the  plane,  and  divide  by  the  length  —  the  quotient  is 
the  power. 

Ex.  Required  the  power  or  equivalent  weight  capa 
ble  of  supporting  a  load  of  350  Ibs.  upon  a  plane  of  1  ID 
12,  or  3  feet  in  height  and  36  feet  in  length. 


—  =  29  16  Ibs.,  or——  =  29-16  Ibs.  power,  as  before 
12  26 


THE    WEDGE. 

The  wedge  is  a  double  inclined  plane ;  consequently, 
its  principles  are  the  same.  Hence,  when  two  bodies 
are  forced  asunder  by  means  of  the  wedge,  in  a  direction 
parallel  .to  its  head,  multiply  the  resisting  power  by 
half  the  thickness  of  the  head  or  back  of  the  wedge,  and 
divide  the  product  by  the  length  of  one  of  its  inclined 
sides  ;  the  quotient  is  the  force  equal  to  the  resistance. 

Ex.  The  breadth  of  the  back  or  head  of  a  wedge 
being  3  inches,  its  inclined  sides  each  10  inches,  re 


MECHANICS.  73 

quired  the  power  necessary  to  act  upon  the  wedge  so  aa 
to  separate  two  substances  whose  resisting  force  ia 
equal  to  150  Ibs 


10 

Note.  —  When  only  ore  of  the  bodies  is  movable,  the  whole 
breadth  of  the  wedge  is  ;aken  for  the  multiplier. 


THE    SCREW. 

The  screw  is  another  modification  of  the  inclined 
plane,  and  it  may  be  said  to  remove  the  same  kind  of 
practical  inconveniences  incidental  to  the  use  of  the 
latter,  that  the  pulley  does  in  reference  to  the  simple 
lever.  The  lever  is  very  limited  in  the  extent  of  its 
action ;  so  is  the  inclined  plane.  But  the  pulley  multi- 
plies the  extent  of  the  action  of  the  lever,  by  presenting, 
in  effect,  a  series  of  levers  acting  in  regular  succession ; 
and  just  such  a  purpose  is  effected  by  the  screw.  It 
multiplies  the  extent  of  the  action  of  the  inclined  plane, 
by  presenting,  in  effect,  a  continued  series  of  planes. 

The  screw,  in  principle,  is  that  of  an  inclined  plane 
wound  round  a  cylinder,  which  generates  a  spiral  of 
uniform  inclination,  each  revolution  producing  a  rise 
or  traverse  motion  equal  to  the  pitch  of  the  screw,  or 
distance  between  the  two  consecutive  threads,  —  the 
pitch  being  the  height  or  angle  of  inclination  and  the 
circumference  the  length  of  the  plane.  Hence,  the  me- 
chanical advantage  is,  as  the  circumference  of  the  circle 
described  by  the  lever  where  the  power  acts  is  to  the 
pitch  of  the  screw,  so  is  the  force  to  the  resistance  in 
principle. 

Ex.  Required  the  effective  power  obtained  by  a 
screw  of  I  inch  pitch,  and  moved  by  a  force  equal  to 
50  Ibs.  at  the  extremity  of  a  lever  30  inches  in  length* 

fX2x  3-1416  XSO 
875 


4  MECHANICS. 

JKc.  2.  Required  the  power  necr.ssa.ry  to  ov*?/crrne  n 
resistance  eq-ial  to  7000  Ibs.  by  a  screw'of  1^  incii  pitch 
and  moved  by  a  lever  25  inches  in  length. 

7000  x  1-25 

=  55-73  IDS.  power. 

25x2x3-1416 

In  the  case  of  a  screw  acting1  on  the  periphery  of  a 
toothed  wheel,  the  power  is  to  the  resistance  as  the 
product  of  the  circle's  circumference  described  by  the 
winch  or  lever,  and  radius  of  the  wheel,  to  the  pro- 
duct of  the  screw's  pitch  and  radius  of  the  axle  or  point 
whence  the  power  is  transmitted ;  but  observe  that,  if 
the  screw  consist  of  more  than  one  thread,  the  apparent 
pitch  must  be  increased  so  many  times  as  there  are 
threads  in  the  screw.  Hence,  to  find  what  weight  a 
given  power  will  equipoise, 

Kulf.  —  Multiply  together  the  radius  of  the  wheel 
the  length  of  the  lever  at  which  the  power  acts,  the 
magnitude  of  the  power,  and  the  constant  number 
(r2£'J2 ;  divide  the  product  by  the  radius  of  the  axle 
into  the  pitch  of  the  screw,  and  the  quotient  is  the 
weight  that  the  power  is  equal  to. 

Ex.  What  weight  will  be  sustained  in  equilibria  by  a 
power  of  100  Ibs.  acting  at  the  end  of  a  lever  24  inches 
in  length,  the  radius  of  the  axle,  or  point  whence  the 
power  is  transmitted  being  8  inches,  the  radius  of  the 
wheel  14  inches,  the  screw  consisting  of  a  double 
tli  read,  and  the  apparent  pitch  equal  |  of  an  inch. 

14  X  24  x  100  X  6-2832 

=  21 11 1-55  Ibs.  the  power  sustained. 

•625  x  2  x  8 

Note.  —  It  is  estimated  that  about  one  third  more  power  must 
DC  added,  to  overcome  the  friction  of  the  screw  when  loaded, 
than  is  necessary  to  constitute  a  balance  between  power  ana 
weight. 


CONTINUOUS    CIRCULAR   MOTION. 


OF  CONTINUOUS   CIRCULAR   MOTION 

IN  mechanics,  circular  motion  is  transmitted  by  means 
of  wheels,  drums,  or  pulleys;  and  accordingly  as  the 
driving  and  driven  are  of  equal  or  unequal  diameters, 
so  are  equal  or  unequal  velocities  produced.  Hence  the 
principle  on  which  the  following  rules  are  founded. 

1.    When  Time  is  not  taken  into  Account. 

Rule.  —  Divide  the  greater  diameter,  or  number  of 
teeth,  by  the  lesser  diameter  or  number  of  teeth  ;  and 
the  quotient  is  the  number  of  revolutions  the  lesser  will 
make,  for  one  of  the  greater. 

Ex.  How  many  revolutions  will  a  pinion  of  20  teeth 
make,  for  1  of  a  wheel  with  125?  ^ 

125  —  20  =  6-25  or  6£  revolutions. 

To  find  the  number  of  revolutions  of  the  last,  to  one 
of  the  first,  in  a  train  of  wheels  and  pinions. 

Rule. — Divide  the  product  of  all  the  teeth  in  the 
driving  by  the  product  of  all  the  teeth  in  the  driven ; 
and  the  quotient  equal  the  ratio  of  velocity  required. 

Ex.  1.  Required  the  ratio  of  velocity  of  the  last,  to  1  of 
the  first,  in  the  following  train  of  wheels  and  pinions ; 
viz.,  pinions  driving,  —  the  first  of  which  contains  10 
teeth,  the  second  15,  and  third  18.  Wheels  driven  first, 
15  teeth,  second,  25,  and  third,  32. 

=  225  of  a  revolution  the  wheel  will  mak«  to 

15  X  25  X  32 

one  of  the  pinion. 

Ex.  2.  A  wheel  of  42  teeth  giving  motion  to  one  of 
12,  on  which  shaft  is  a  pulley  of  21  inches  diametef 

7* 


76  CONTINUOUS    CIRCULAR    MOTION. 

driving  one  of  G;  required  the  number  of  revelations  of 
the  last  pulley  to  one  of  the  first  wheel. 

4'*  X  CT1 

— — -  —  12-25  or  124  revolutions. 

12x6 

2.    If  hen  Time  must  be  regarded. 

Rule.  —  Multiply  the  diameter  or  number  of  teeth  :.n 
the  driver,  by  its  velocity  in  any  given  time,  and  divide 
the  product  by  the  required  velocity  of  the  driven  ;  the 
quotient  equal  the  number  of  teeth  or  diameter  of  the 
driven,  to  produce  the  velocity  required. 

Ex.  1.  if  a  wheel,  containing  84  teeth,  makes  20 
revolutions  per  minute,  how  many  must  another  contain, 
to  work  in  contact,  and  make  GO  revolutions  in  the 
same  time? 

84x20 


GO 


-=28  teeth. 


Ex.  2.  From  a  shaft  making  45  revolutions  per  mm- 
ute,  and  with  a  pinion  9  inches  diameter  at  the  pitch 
line,  I  wish  to  transmit  motion  at  15  revolutions  per 
minute ;  what,  at  the  pitch  line,  must  be  tbe  diameter 
of  the  wheel. 

45x9 

=  27  inches. 

15 

Ex.  3.  Required  the  diameter  of  a  puliey  to  make  16 
revolutions  in  the  same  time  as  one  of  24  inches  mak- 
ing ;$G. 

24x36 

=  54  inches. 

16 

Tht  distance  between  the  centre*  and  vthcities  cf  two 
wheels  being  given,  to  find  their  proper  dianuters. 

Rule.  —  Divide  the  greatest  velocity  by  the  least;  the 
quotient  is  the  ratio  of  diameter  the  wheels  must  bear 
to  each  other. 


CONTIGUOUS    CIRCULAR    MOTION.  77 

Hence,  divide  the  distance  between  the  centres  by 
/he  ratio  -1-  1  ;  the  quotient  equal  the  radius  of  the 
smaller  wheel ;  and  subtract  the  radius  thus  obtained 
from  the  distance  between  the  centres;  the  remainder 
equal  the  radius  of  the  other. 

Ex.  1.  The  distance  of  two  shafts  from  centre  to 
centre  is  50  inches,  and  the  velocity  of  the  one  25  rev- 
olutions  per  minute,  the  other  is  to  make  80  in  the  same 
time ;  the  proper  diameters  of  the  wheels  at  the  pitch 
lines  are  required. 

50 

80-^-25  =  3-2,  ratio  of  velocity,  and =  11-9.  the  radius 

3-2  +1 

of  the  smaller  wheel ;  then  50  —  1 1  -9  =  38-1 ,  radius  of  larger ; 
their  diameters  are  11 -9  x2  =23-8  and  38-1  X  2  =  76-2  inches. 

To  obtain  or  diminish  an  accumulated  velocity  by 
means  of  wheels,  pinions,  or  wheels,  pinions,  and  pulley^ 
it  is  necessary  that  a  proportional  ratio  of  velocity 
should  exist,  and  which  is  thus  attained :  multiply  the 
given  and  required  velocities  together ;  and  the  square 
root  of  the  product  is  the  mean  or  pioportionate  velo- 
city. 

Ex.  Let  the  given  velocity  of  a  wheel  containing  54 
teeth  equal  16  revolutions  per  minute,  and  the  given 
diameter  of  an  intermediate  pulley  equal  25  inches,  to 
obtain  a  velocity  of  81  revolutions  in  a  machine ;  re- 
quired the  number  of  teeth  in  the  interrr.  ediate  wheel 
and  diameter  of  the  last  pulley. 

-y/81  X  16  =  36  mean  velocity. 

=  24  teeth  and -^-~ — =11-1   inches,  diameter  of 

36      *  81 

pulley. 


To  determine  the  proportion  of  wheels  for  screw-cut- 
ting by  a  lathe. 

TT?  a  Mhe  properly  adapted,  screws  to  any  degree  of 
Ditch,  or  number  of  threads  in  a  given  length,  may  be 


/8  CONTINUOUS    CIRCULAR    MOTION. 

cut  by  means  of  a  leading  screw  of  any  given  pitch,  ac- 
companied with  change  wheels  and  pinions;  coarse 
pitches  being  effected  generally  by  means  of  one  wheel 
and  one  pinion  with  a  carrier,  or  intermediate  wheel, 
which  cause  no  variation  or  change  of  motion  to  take 
place.  Hence  the  following 

Rule. — Divide  the  number  of  threads  in  a  given 
length  of  the  screw  which  is  to  be  cut,  by  the  number 
of  threads  in  the  same  length  of  the  leading  screw  at- 
tached to  the  lathe ;  and  the  quotient  is  the  ratio  that 
the  wheel  on  the  end  of  the  screw  must  bear  to  that  on 
.the  end  of  the  lathe  spindle. 

Ex.  Let  it  be  required  to  cut  a  screw  with  5  threads 
in  an  inch,  the  leading  screw  being  of  £  inch  pitch,  or 
containing  2  threads  in  an  inch;  what  must  be  the  ratio 
of  wheels  applied  ? 

5  +  2  =  2-5,  the  ratio  they  must  bear  to  each  other. 

Then  suppose  a  pinion  of  40  teeth  be  fixed  upon  for 
the  spindle,  — 

40  x  2-5  =  100  teeth  for  the  wheel  on  the  end  of  the  screw 

But  screws  of  a  greater  degree  of  fineness  than  about 
8  threads  in  an  inch  are  more  conveniently  cut  by  an 
additional  wheel  and  pinion,  because  of  the  proper  de- 
gree of  velocity  being  more  effectively  attained;  and 
these,  on  account  of  revolving  upon  a  stud,  are  com- 
monly designated  the  stud-wheels,  or  stud-wheel  and 
pinion ;  but  the  mode  of  calculation  and  ratio  of  screw 
are  the  same  as  in  the  preceding  rule.  Hence,  all  that 
is  further  necessary  is  to  fix  upon  any  3  wheels  at 
pleasure,  as  those  for  the  spindle  and  stud-wheels; 
then  multiply  the  number  of  teeth  in  the  spindle-wheel 
by  the  ratio  of  the  screw,  and  by  the  number  of  teeth  in 
that  wheel  or  pinion  which  is  in  contact  with  the  wheel 
on  the  end  of  the  screw ;  divide  the  product  by  the  stud- 
wheel  in  contact  with  the  spindle-wheel ;  and  the  quo- 
tient is  the  number  of  teeth  required  in  the  wheel  on  the 
end  of  the  leading  screw. 


CONTINUOUS    CIRCULAR    MOTION.  TtJ 

JKx.  Suppose  a  screw  is  required  to  be  cut  containing 
25  threads  in  an  inch,  the  leading  screw,  as  before, 
having  two  threads  in  an  inch,  and  that  a  wheel  of  (JO 
teetn  is  fixed  upon  for  the  end  of  the  spindle,  20  for  the 
pinion  in  contact  with  the  screw-wheel,  and  100  for  that 
in  contact  with  the  wheel  on  the  end  of  the  spindle; 
required  the  number  of  teeth  in  the  wheel  for  the  end 
of  the  leading  screw. 

=  ,«,  teeth. 


100 

Or  suppose  the  spindle  and  screw-wheels  to  be  those 
fixed  upon,  also  any  one  of  the  stud-  wheels,  to  find  the 
number  of  teeth  in  the  other. 


,»  teeth,  or          ..        ^  ,„(„«*. 


, 
150  X  100  150 


60 


CONTINUOUS    CIRCULAR   MOTION 


Table  of  Change  Wheels  for  Screw-cutting  ;  the  leading 
Screw  being  of  £  inch  pilch,  or  containing  2  threads  in 
an  inch. 


Numb.of 

Number  of 

Number  of 

S3 

teeth  in 

S3 

teeth  in 

G 

teeth  in 

CD 

i 

, 

•9 

JS     • 

i 

gfc 

|| 

£ 

i 

1 

i 

«1 

|1 

ll 
c  ^ 

<o 

£   « 

12 

1 

%-.  £ 

"O 

g 

Si 

?  • 

0 

C  » 

13 
H 

o  i 

s* 

°  8 

a. 

be 

°    0 

£"§ 

E  i 

be 

°  y 

'S. 

11 

> 

bo 

2^  *v 

_^ 

e  __. 

.Js  ""S 

<D  — 

—  "5. 

C    03 

5  -4 

A   0 

_: 

"3  ^ 

S3  to 

.£  —! 

£  ~ 

•^   JJ 

~3    3> 

£.c 

11 

.Is 

£  js 

Id   ^ 

S  _= 

!j 

£>c 

~"S 

"r  ^ 

..3  - 

51 

,31 

11 

31 

£f 

£'i 

a« 

II 

31 

^1 

II 

il 

1 

80 

40 

84 

40 

55 

20 

60 

19 

50 

95 

20, 

100 

u 

80 

50 

84 

90 

85 

20 

90 

194 

80 

120 

20 

130 

14 

80 

60 

84 

60 

70 

20 

75 

•20 

60 

100 

20 

120 

11 

80 

70 

i 

90 

90 

20 

95 

20* 

40 

90 

20 

90 

9 

80 

90 

40 

60 

20 

65 

21 

80 

120 

20 

140 

24 

so 

90 

10 

60 

75 

20 

80 

22 

60 

110 

20 

120 

24 

80 

100 

104 

50 

70 

20 

75 

22* 

80 

120 

20 

150 

2| 

80 

110 

11 

60 

55 

20 

120 

80 

130 

20 

140 

3 

80 

120 

12 

90 

90 

20 

120 

23| 

40 

95 

20 

100 

34 

80 

130 

60 

85 

20 

90 

24 

65 

120 

20 

130 

34 

80 

140 

13 

90 

90 

20 

130 

25 

60 

100 

20 

150 

31 

80 

150 

60 

90 

20 

90 

25J 

30 

85 

20 

90 

4 

40 

80 

131 

80 

100 

20 

110 

26 

70 

130 

20 

140 

44 

40 

85 

14 

90 

90 

20 

140 

27 

40 

90 

20 

120 

44 

40 

90 

144 

60 

90 

20 

95 

k^^i 

40 

100 

20 

110 

41 

40 

95 

15 

90 

90 

20 

150 

28 

75 

140 

20 

150 

40 

100 

16 

60 

80 

20 

120 

28^ 

30 

90 

20 

95 

54 
6 

40 
40 

110 
120 

lit 

80 
80 

100 
110 

20 

20 

130 
120 

30 
32 

70 
30 

140 

80 

20 
20 

150 
120 

$h 

40 

130 

17 

45 

85 

20 

90 

33 

40 

110 

20 

120 

40 

140 

174 

80 

100 

20 

]4( 

34 

30 

85 

20 

120 

? 

40 
30 

150 
120 

18 

40 
80 

60  1  20  J120 
100120  1150 

35 
36 

60  J140 
301  90 

20 
20 

150 
120 

CONTINUOUS    CIRCULAR    MOTION.  OA 

Table  by  which  to  determine  the  Number  of  Teeth,  o? 
Pitch  of  Small  Whtds,  by  what  is  commonly  called  the 
Manchester  Principle. 


Diametral 

Circular 

Diametral 

Circular 

pitch. 

pitch. 

pitch. 

pitch. 

3 

1-047 

9 

•349 

4 

•785 

10 

•314 

5 

•648 

12 

•262 

6 

•524 

14 

•224 

7 

•449 

16 

•196 

8 

•393 

20 

•157 

jKr.  1.  Required  the  number  of  teeth  that  a  whee* 
of  16  inches  diameter  will  contain  of  a  10  pitch. 

16  X  10=  160  teeth,  and  the  circular  pitch  =-314  inch. 

Ex.  2.  What  must  be  the  diameter  of  a  wheel  for  a 
9  pitch  of  126  teeth  ? 

126 
— =  14  inches  diameter,  circular  pitch  -349  inch. 

Note.  —  The  pitch  is  reckoned  on  the  diameter  of  the  wheel 
instead  of  the  circumference,  and  designated  wheels  of  8  pitch. 
12  pitch,  &c. 

Strength  of  the  Teeth  of  Cast  Iron  Wheels  at  a  given 
Felociti/. 


Pitch 

of  teeth 
in  inches 

Thicknew 
of  teeth 
in  inches. 

Breadth 
of  teeth 
in  inches. 

Strength  of  teeth  in  horse-pcnver  at 

3  feet  per 

4  feet  per 

6  feet  per 
second. 

8  feet  p-F 
second. 

3-99 

1-9 

7-6 

20-57 

27-43 

41-14 

54-85 

3-78 

1-8 

7-2 

17-49 

23-32 

34-98 

46-64 

3-57 

1-7 

6-8 

14-73 

19-65 

29-46 

39-28 

3-36 

1-6 

6-4 

12-28 

16-38 

24-55 

32-74 

3-15 

1-5 

6 

10-12 

13-50 

20-24 

26-98 

2-94 

1-4 

5-6 

8-29 

10-97 

16-44  * 

21-92 

2-73 

1-3 

5'2 

6-58 

8-78 

13-16 

17-54 

2-52 

1-2 

4'8 

5-18 

6-91 

10-36 

13-81 

2-31 

1-1 

4'4 

3-99 

5-32 

7-98 

10-64 

2-1 

1-0 

4 

3-00 

4-00 

6-00 

8-00 

1-89 

•9 

3-6 

2-18 

2-91 

4-36 

5-81 

168 

•8 

3-2 

1-53 

2-04 

3-06 

3-08 

1-47 

•7 

2-8 

1-027 

1-37 

2-04 

2-72 

1-26 

•6 

2-4 

•64 

•86 

1-38 

1-84 

1-05 

•5 

2 

•375 

•50 

•75 

1-00 

82  ritAcj  (,AL    PROPERTIES    OF    WATER. 


PRACTICAL  PROPERTIES   OF  WATER 


BY  analysis  it  is  ascertained,  that  water  is  composed 
of  the  gases  oxygen  and  hydrogen  in  a  state  of  chemical 
anion ;  its  distinguishing  properties,  like  that  of  othei 
liquids,  being  nearly  incompressible  gravity,  capability 
of  flowing,  and  constant  tendency  to  press  outwards  in 
every  direction ;  also  that  of  being  easily  changed  by 
the  absorption  of  caloric  to  an  aeriform  state  of  any  re- 
quired density  or  degree  of  elastic  force:  hence  the 
principle  of  the  hydraulic  press,  the  water-wheel,  the 
steam  engine.,  &c 

Effects  produced  by  Water  in  Us  natural  State. 

Because  of  liquids  possessing  the  properties  of  gravity 
and  capability  of  flowing  freely  in  every  direction,  sides 
of  vessels,  flood-gates,  sluices,  &c..  sustain  a  pressure 
equal  to  the  product  of  the  area  multiplied  by  half  the 
depth  of  the  fluid,  and  by  its  gravity  in  equal  terms  of 
unity. 

But  when  a  sluice  or  opening  through  which  a  liquid 
*nay  issue  is  under  any  given  continued  head,  the  pres- 
sure is  equal  the  product  of  the  area  multiplied  into  the 
height,  from  the  centre  of  the  opening  to  the  surface  of 
the  fluid. 

Ex.  1.  Required  the  pressure  of  water  on  the  sides 
of  a  cistern  18  feet  in  length,  13  in  width  and  9  in 
dapth. 

The  terms  of  measurement  or  unity  are  in  feet,  1  cubic  foot  ot 
water  .-=  (i-2-5  Ibs. ;  hence  18  x  9  X  2  +  13  X  9  X  2  —  558  X 
4-5  x  62-  5  =  156937-5  Ibs.  weight  of  water  on  bottom  =  18  X 
13x9x62-5  =131625  Ibs. 

Ex.  2.  Required  the  pressure  on  a  sluice  3  feet  square, 
and  its  centre  30  feet  from  the  surface  of  the  water 

3  x  3  x  30  x  62-5  =  16875  Ibs.  pressure. 


PRACTICAL    PROPERTIES    OF    WATER.  83 

The  weight  of  water  or  other  fluid  is  as  the  quantity 
but  the  pressure  exerted  is  as  the  vertical  height.  Hence, 
as  fluids  press  equally  in  every  direction,  any  vessel 
containing  a  fluid  sustains  a  pressure  equal  to  as  many 
times  the  weight  of  the  column  of  greatest  height  of 
that  fluid,  as  trie  area  of  the  vessel  is  to  the  sectional 
area  of  the  column. 

JEr.  Let  a  cubical  vessel,  whose  sides  are  each  4 
square  feet,  have  a  tube  inserted  1  inch  in  diameter,  and 
6  feet  in  height,  and  let  both  vessel  and  tube  be  filled 
with  water;  required  the  whole  weight  of  the  water 
therein  contained,  and  also  the  whole  pressure  exerted 
intending  to  burst  the  vessel. 

Cubic  contents  of  the  vessel  =  8  feet,  and  each  foot  =  62-5  Ibs. ; 
then  62-5  X  8  =  500  area  of  pipe's  section  =  -7854  inches,  and 
height  72  inches,  also  a  cubic  inch  of  water  =  -03617  Ibs.j 
hence,-7854  X  72  x  '03617  =  2  Ibs.  +  500  =  602  Ibs.,  total 
weight  of  the  water. 

Again  ;  the  whole  height  of  the  column  =  96  inches  ;  then  -7854 
X  96  X  -036 17  =  2-33  Ibs.,  pressure  of  column  on  an  equal 

14*  x  4  X  6  side3 

area.    144  square  inches  =  1  square  foot,  and 

•7854 

=  4400*4  times  the  area  of  the  pipe's  diameter  in  the  whole 
surfnce  ;  therefore,  4400-4  X  2-33  =  10253  lbs.;  or  total  amount 
of  pressure  exerted. 

To  find  the  velocity  of  water  issuing  a  circular  orifice 
ai  any  given  depth  from  the  surface. 

Rule.  -  Multiply  the  square  root  of  the  height  or 
depth  to  the  centre  of  the  orilice  by  8-1 ;  and  the  product 
is  the  velocity  of  the  issuing  fluid  in  feet  per  second. 

JE.r.  Required  the  velocity  of  water  issuing  through 
an  orifice  under  a  head  of  11  feet  from  the  surface. 

V  11  =  3-3166  X  8-1  =  26-864  feet,  velocity  per  second. 
In  the  discharge  of  water  by  a  rectangular  aperture  in 
the  side  of  a  reservoir,  and  extending  to  the  surface, 
the  velocity  varies  nearly  as  the  square  root  of  the  height, 
ana  the  quantity  discharged  per  second  equal  |rds  of 
the  velocity  due  to  the  mean  height,  allowing  for  the 
8 


84  PRACTICAL    PROPERTIES    OF    WATER. 

contraction  of  the  fluid  according  to  the  form  of  tfi£ 
opening,  which  renders  the  coefficient  in  this  case  equal 
to  5-1  ;  whence  the  following  general  rules. 

1.  When  the  aperture  extends  to  the  surface  of  the 
fluid.     Multiply  the  area  of  the  opening  in  feet  by  the 
square  root  of  its  depth  also  in  feet  and  that  product  by 
5'1  :  then  will  :;rdsof  the  last  product  equal  the  quantity 
discharged,  in  cubic  feet,  per  second. 

2.  •  When  the  aperture  is  under  a  given  head.     Mul- 
tiply the  area  of  the  aperture,  in  feet,  by  the  square  root 
of  the  depth,  also  in  feet,  and  by  5-1  ;  the  product  is  the 
quantity  discharged,  in  cubic  feet,  per  second. 

Ex.  1.  Required  the  quantity  of  water  in  cubic  feet 
per  second,  discharged  through  an  opening  in  the  side 
of  a  dam  or  weir,  the  width  .or  length  of  the  opening 
being  G£  feet,  and  depth  1)  inches,  or  *75  of  a  foot. 

Square  root  of  -75  =  -866. 

cubic  feet 


Ex.  2.  What  would  be  the  quantity  discharged 
through  the  above  opening,  if  under  a  head  of  water  4 
feet  in  height  ? 

Square  root  of  4  =  2,  and  2x5-1  =  10-2  feet,  velocity  of  the 
water  per  second.  And  6-5  X  -75  x  2  x  5  1  ==  49-725  cubic 
feet  discharged  in  the  same  time. 

The  combined  properties  of  gravity  and  fluidity  which 
water  possesses,  renders  it  so  available  as  a  source  of 
motive  power;  gravity  being  the  property  ,by  which  the 
power  is  produced,  and  fluidity  that  by  which  it  is  so 
commodiously  qualified  to  the  various  modifications  in 
which  it  is  employed. 

Water,  it  is  ascertained,  is  subject  to  the  same  laws 
of  gravity  as  those  of  solid  bodies,  and  thereby  accumu- 
lates velocity  or  effect  in  an  equal  ratio  when  filling 
through  an  equal  space,  or  descending  from  an  equal 
height.  Hence,  the  velocity  attained  is  as  the  square 
root  of  the  height  of  its  fall  ;  and  it  is  now  quite  satis- 


PRACTICAL    PROPERTIES    OF   WATER.  85 

factorily  decided,  that,  because  of  the  non-elastic  prop- 
erty of  water,  its  greatest  is  obtained  when  acting  by 
gravity  throughout  its  whole  height,  whether  it  be  ap- 
plied on  a  water-wheel,  turbine,  or  other  machine 
through  which  circular  motion  is  to  be  the  immediate 
result. 

In  regard  to  water-wheels,  and  other  machines 
through  which  motion  is  produced  by  the  effort  ot 
water,  much  discrepancy  of  opinion  has,  until  lately, 
existed,  both  as  to  form  and  velocity,  besides  other 
essential  points  requisite  in  gaining  a  maximum  of 
effect  with  the  least  possible  strain ;  but  these  doubts 
are  now  in  a  great  measure  removed  through  experi- 
ments by  the  Franklin  Institute  in  this  country,  added 
to  ti  ose  in  France  by  Morin,  and  the  results  of  a  pa 
tentc  d  machine  by  Whitelaw  and  Stirrat,  Scotland, 
combined  with  pertinent  observations  and  remarks  by 
interested  parties  in  this  as  well  as  other  countries. 
Hence  have  been  deduced  the  following  demonstrative 
conclusions :  — 

1.  That,  to  gain  a  maximum  of  effect  by  a  horizontal 
water-wheel,  the  water  must  be  laid  upon  the  wheel  on 
the  stream  side,  and  the  diameter  of  the  wheel  so  pro- 
portioned to  the  height  of  the  fall,  that  the  water  may 
may  be  laid  on  about  52$   degrees  distant  from  the 
summit  uf  the  wheel,  or  the  height  of  the  fall,  being  1 
the  height  or  diameter  of  the  wheel  equal  1-108. 

2.  That  the  periphery  of  a  water-wheel  ought  to  move 
ai.  a  velocity  equal  to  about  twice  the  square  root  of  the 
fall  of  the  water  in  feet  per  second,  and  the  number  of 
buckets  equal  SM  times  the  wheel's  diameter  in  feet ; 
also,   that    precautionary   means   be    adopted   for  the 
escape  of  the  air  out  of  the  buckets,  either  by  making 
the  stream  of  water  a  few  inches  narrower  than  the 
wheel,  or  otherwise. 

3.  That,  because  of  water  producing  a  less  efficient 
power  by  impulse  than  gravity,  turbines,  or  machines 
through  which  the  motion  is  obtained  by  reaction,  are 
greatly  preferable  to  undershot,  or  low-breast  wheels. 


66  PRACTICAL    PROPERTIES    OF  WATER. 

4.  That   a  head  of  water  is  required   sufficient  to 
cause  the  velocity  of  its  flowing  to  be  as  3  to  2  of  the 
wheel ;   i  of  the  wheel's  diameter  being  an  approximate 
height,  near  enough  for  practical  purposes. 

5.  That  the  effective  power  of  a  wheel  constructed 
according  to  these  restrictions,  is  equal  to  the  product 
of  the  number  of  cubic  feet  and  velocity  in  feet  per 
minute,  multiplied  into  -001325. 


Example  for  general  Rluslration. 

Suppose  a  fall  of  water  25  feet  in  height,  over  which 
is  delivered  112  cubic  feet  per  minute;  required  the 
various  peculiar  requisites  for  a  wheel  *o  be  in  accord- 
ance with  the  preceding  rules. 

1st.  25  X  1-08  =  27  feet,  the  wheel's  diameter. 
2d.    V  tb  x  2  =  10  feet,  velocity  of  the  wheel 

in  feet  per  second. 
Also  :  27  X  2-1  =  5fr7,  say  57  buckets, 

3d.    27  —  9  =  3  feet,  head  of  water  required. 
4th.    lit  x  10  X  60  X  -0013°25  =  89  horses'  power. 

The  turbine  of  Fourneyron,  in  France,  and  the 
patented  water-mill  of  Whitelaw  and  Stirrat,  Scotland, 
have,  of  late  years,  attracted  a  considerable  share 
of  public  attention ;  their  simplicity  of  construction 
and  asserted  effects  in  like  situations,  being  equal  to 
those  of  the  best  applied  water-wheels.  In  their  manner 
of  construction  they  differ,  but  in  principle  they  are  the 
same  ;  the  action  of  each  being  created  by  a  centrifugal 
and  tangential  force,  caused  by  the  weight  or  impulsion 
of  a  column  of  water  whose  height  or  altitude  is  equal 
to  twice  the  height  of  the  fall  due  to  the  water's  velo- 
city ;  and  in  order  to  produce  a  maximum  of  effect  in 
father  the  one  or  the  other  by  the  pressure  and  centrif- 
ugal force  of  the  effluent  water,  it  is  necessary  that  the 
emitting  tubes  or  helical  channels  of  the  machine  be  so 
curved  that  the  apertures  shall  be  in  a  right  line  with 
the  radius  of  the  wheel. 


STEAM    POWER.  87 

1.  That  turbines  are  equally  adapted  to  great  as  to 
small  waterfalls. 

2.  That  they  are  capable  of  transmitting  a  useful 
effect  to  from  70  to  78  per  cent,  of  the  absolute  power. 

3.  That  their  velocities  may  vary  considerably  from 
the  maximum  effect,  without  differing  sensibly  from  it. 

4.  That  they  will  work  nearly  as  effectually  when 
drowned   to  the  depth  of  6  feet  as  when   free,  and, 
consequently,  they  will  make  use  of  the  whole  of  the 
fall  when  placed  below  the  level  of  extreme  low  water. 

5.  That  they  receive  variable  quantities  of  water, 
without  altering  the  ratio  of  the  power  to  the  effect. 


STEAM   POWER. 

THERE  is  no  application  of  science  to  the  arts  of 
more  importance,  and  more  extensive  in  its  effects,  than 
that  of  the  employment  of  steam  for  driving  all  kinds 
of  machinery.  It  is  not  my  intention  to  enter  into  the 
details  of  the  power  of  steam  or  the  steam-engine,  but 
to  give  some  practical  rules,  the  utility  of  which  have 
been  tested. 

Steam  is  of  great  utility  as  a  productive  source  of 
motive  power;  in  this  respect,  its  properties  are,  elastic 
force,  expansive  force,  and  reduction  by  condensation. 
Elastic  signifies  the  whole  urgency  or  power  the  steam 
is  capable  of  exerting  with  undiminished  effect.  By 
expansive  force  is  generally  understood  the  amount  of 
diminishing  effect  of  the  steam  on  the  piston  of  a 
steam-engine,  reckoning  from  that  point  of  the  stroke 
where  the  steam  of  uniform  elastic  force  is  cut  off;  but 
it  is  more  properly  the  force  which  steam  is  capable  of 
exerting,  when  expanded  to  a  known  number  of  times 
its  original  bulk.  And  condensation,  here  understood, 


88 


STEAM    POWER 


is  tho  abstraction  or  reduction  of  heat  by  another  body 
and  conrequently  not  properly  a  contained  property  of 
the  steam,  but  an  effect  produced  by  combined  ao-ency 
in  which  stearn  is  the  principal ;  because  any  colder 
body  will  extract  the  heat  and  produce  condensation, 
but  steam  cannot  be  so  beneficially  replaced  by  any 
other  fluid  capable  of  maintaining  equal  results. 

The  rules  formed  by  experimenters,  as  corresponding 
with  the  results  of  the;r  experiments  on  the  elastic 
force  of  steam  at  given  temperatures,  vary,  but  ap- 
proximate so  closely,  that  the  following  rule,  because 
of  being  simple,  may,  in  practice,  be  taken  in  preference 
to  any  other. 

Rule.  —  To  the  temperature  of  the  steam,  in  degrees 
of  Fahrenheit,  add  100;  divide  the  sum  by  177 ;  and  the 
6th  power  of  the  quotient  equal  the  force  in  inches  of 
mercury. 

Ex.  Required  the  force  of  steam  corresponding  to  a 
temperature  of  312°. 


312  4- 100 
177 


=  2-S2776  =  159  inches  of  mercury. 


To  estimate  the  amount  of  advantage  gained  by  using 
steam  expansively  in  a  steam-engine. 

When  steam  of  a  uniform  elastic  force  is  employed 
throughout  the  whole  ascent  or  descent  of  the  piston, 
the  amount  of  effect  produced  is  as  the  quantity  of 
steam  expended.  But  let  the  steam  be  shut  off  at  any 
portion  of  the  stroke,  — say,  for  instance,  at  one-half,  — 
it  expands  by  degrees  until  the  termination  of  the 
stroke,  and  then  exerts  half  its  original  force ;  hence 
an  accumulation  of  effect  in  proportion  to  the  quantity 
of  steam. 

Ru!e.  —  Divide  the  length  of  the  stroke  by  the  dis- 
tance or  space  into  which  the  dense  steam  is  admitted, 
and  find  the  hyperbolic  logarithm  ot  the  quotient,  to 
which  add  1 ;  and  the  sum  is  the  ratio  of  the  gain. 


STEAM    POWER. 


89 


Ex.   Suppose  an  engine  with  a  stroke  of  6  feet,  and 
uie  steam  cut  off'  when  the  piston  has  moved  through 
•;  required  the  ratio  of  gain  by  Uniform  and  expansive 
force. 

G-f-2  =  3 ;  hyperbolic  logarithm  of  3  =  1-0986  -f 1  =  2-0986, 
ratio  of  effect;  that  is,  supposing  the  whole  effect  of  the 
steam  to  be  3,  the  effect  by  the  steam  being  cut  off  at 
I  =  2-0986. 

Again ;  let  the  greatest  elastic  force  of  steam  in  the 
cylinder  of  an  engine  equal  48  Ibs.  per  square  inch, 
and  let  it  be  cut  off  from  entering  the  cylinder  when 
Jie  piston  has  moved  4-i  inches,  the  whole  stroke  being 
18 ;  required  an  equivalent  force  of  the  steam  through- 
out the  whole  stroke. 

18  —  4-5  =  4,  and  48  —  4  =  12. 

Logarithm  of  4-f  1  =2-38629. 

Then  9-38629  X  12  =  28-635  Ibs.  per  square  inch. 

In  regard  to  the  other  case  of  expansion,  when  the 
temperature  is  constant,  the  bulk  is  inversely  as  the 
pressure;  thus,  suppose  steam,  at  30  Ibs.  per  square 
inch,  required  its  bulk  to  that  of  original  bulk,  when 
expanded  so  as  to  retain  a  pressure  equal  to  that  of  the 
atmosphere,  or  15  Ibs. 


15  +  30 
15 


=  3  times  its  original  bulk. 


It  is  because  of  the  latent  heat  in  steam,  or  water  in 
an  aeriform  state,  that  it  becomes  of  such  •  essential 
service  in  heating,  boiling,  drying,  &c.  In  the  heating 
of  buildings,  its  economy,  efficiency,  and  simplicity  of 
application,  are  alike  acknowledged ;  the  steam,  being 
simply  conducted  through  all  the  departments  by  pipes, 
by  extent  of  circulation  condenses,  —  the  latent  heat 
being  thus  given  to  the  pipes,  and  diffused  by  radiation. 
In  boiling,  its  efficiency  is  considerably  increased,  if 
advantage  be  taken  of  sufficiently  enclosing  the  fluid, 
and  reducing  the  pressure  on  its  surface,  by  means  of 


90  PRODUCTION    OF    STEAM. 

an  air-pump.  Tins  water  in  a  vacuum  boils  at  about 
a  temperature  of  .to- ;  and  in  sugar-refining,  where 
such  means  are  employed,  the  sirup  is  boiled  at  150: 

Effects  produced  by  Water  in  an  Aeriform  State. 

When  water  in  a  vessel  is  subjected  to  the  action  of 
fire,  it  readily  imbibes  the  heat,  or  fluid  principle  of 
which  the  fire  is  the  immediate  cause,  and,  sooner  or 
later,  according  to  the  intensity  of  the  heat,  attains  a 
temperature  of  212°  Fahrenheit.  If,  at  this  point  of 
temperature,  the  water  be  not  enclosed,  but  exposed  to 
atmospheric  pressure,  ebullition  will  take  place,  and 
steam  or  vapor  will  ascend  through  the  water,  carrying 
with  it  the  superabundant  heat,  or  that  which  the  water 
cannot,  under  such  circumstances  of  pressure,  absorb, 
to  be  retained,  and  to  indicate  a  higher  temperature. 

Water,  in  attaining  the  aeriform  sbite,  is  thus  uni- 
formly confined  to  the  same  laws,  under  every  degree 
of  pressure ;  but,  as  the  pressure  is  augmented,  so  is 
the  indicated  temperature  proportionately  elevated. 
Hence  the  various  densities  of  steam,  and  correspond- 
ing degrees  of  elastic  force. 


PROPERTIES    OF    STEAM. 


91 


Table  of  the  Elastic  Force  of  Slectm,  and  corresponding 
Temperature  of  the  Water  with  which  it  is  in  Contact. 


I'ressure  per 
square  inch, 
atmospheric 
pressure 
included. 

Elastic  Force  in 

Temperature  in  Degrees  of 

Volume 
ol   Steam 
compared 
with  Vol. 
of  Water. 

Inches  of  1 
Mercury. 

Ms  ires  of 
Mercury. 

Fahr. 

Reaum. 

Cent. 

Ibs. 

kilog. 

14-7 

6-668 

30-00 

-762 

212-0 

80-0 

100-0 

1711 

15 

6-80 

30-60 

•778 

212-8 

80-4 

100-4 

1670 

16 

7-26 

32-64 

•829 

216-3 

81-9 

102-4 

1573 

17 

7-71 

34-68 

•880 

219-6 

83-3 

104-2 

1488 

18 

8-16 

36-72 

•932 

222-7 

84-7 

105-9 

1411 

19 

8-62 

38-76 

•984 

225-6 

86-0 

107-6 

1343,., 

20 

9-07 

40-80 

1-037 

228-5 

87-3 

109-2 

1281 

21 

9-52 

42-84 

•089 

231-2 

88-5 

110-7 

1225 

22 

9-98 

44-88 

•140 

233-8 

89-7 

112-1 

1174 

23 

10-43 

46-92 

•192 

236-3 

908 

113-5 

1127 

24 

10-88 

48-96 

•244 

238-7 

91-9 

114-8 

1084 

25 

11-34 

51-00 

•296 

241-0 

93-0 

116-1 

1044 

26 

11-79 

53.04 

•3-18 

243-3 

93-9 

117-4 

1007 

27 

12-25 

55-08 

1400 

245-5 

94-9 

118-6 

973 

28 

12-70 

57-12 

1-452 

247-6 

95-8 

119-8 

941 

29 

13-15 

59-16 

1-503 

249-6 

96-7 

120-9 

911 

30 

13-61 

61-21 

1-555 

251-6 

97-6 

122-0 

883 

31 

14-06 

63-24 

1-607 

253-6 

98-5 

123-1 

857 

°z 

14-51 

65-28 

1-659 

255-5 

99-3 

124-2 

833 

33 

14-97 

67-32 

1-711 

257-3 

100-1 

125-2 

810 

34 

15-42 

69-36 

1-763 

259-1 

100-9 

126-2 

788 

35 

15-87 

71-40 

1-814 

260-9 

101-7 

127-2 

767 

36 

16-33 

73-44 

1-866 

262-6 

102-5 

128-1 

748 

37 

16-78 

75-48 

1-918 

264-3 

103-2 

129-1 

729 

38 

17-23 

77-52 

1-970 

265-9 

104-0 

129-9 

712 

39 

17-69 

79-56 

2-022 

267-5 

104-7 

130-8 

695 

40 

18-14 

81-60 

2-074 

269-1 

105-4 

131-7 

679 

41 

18-59 

83-64 

2-126 

270-6 

106-0 

132-6 

664 

42 

19-05 

85-64) 

2-178 

272-1 

106-7 

133-4 

649 

43 

19-50 

87-72 

1-229 

273-6 

1074 

134-2 

635 

44 

19-96 

89-76 

2-281 

275-0 

108-0 

135-0 

622 

45 

20-41 

91-80 

2-333 

276-4 

108-6 

135-8 

610 

46 

20-86 

93-84 

2-385 

277-8 

109-2 

136-6 

598 

47 

21-32 

95-88 

2-437 

279-2 

109-9 

137-3 

586 

41 

21-77 

97  '»? 

2-489 

280-5 

110-4 

138-1 

575 

49 

22-22 

99-y> 

2-541 

281-9 

111-1 

138-8 

564 

50 

22-68 

102-00 

2-592 

283-2 

11  If 

139-6 

554 

02  PROPERTIES    OF    STEAM. 

The  preceding  table  is  peculiarly  adapter]  for  esti 
mating  the  power  of  steam  engines  on  the  condensing 
principle,  because,  in  such,  the  effective  force  of  the 
Btearn  is  the  difference  between  the  total  force  and  the 
resisting  vapor  retained  in  the  condenser.  The  fol- 
lowing table  is  more  adapted  for  estimating  the  effects 
of  non-condensing  engines;  as,  in  such,  the  atmos- 
pheric pressure  is  not"  generally  taken  into  account, 
engines  of  this  principle  being  supposed  to  work  in  a 
medium:  or,  the  atmospheric  pressure  on  the  boilers, 
to  cause  a  greater  density  of  steam,  is  equal  to  the 
resisting  atmosphere  which  the  effluent  steam  has  to 
contend  with,  on  leaving  the  cylinder. 

Steam,  independent  of  the  heat  indicated  by  an  im- 
mersed thermometer,  also  contains  heat  that  cannot  be 
measured  by  any  instrument  at  present  known,  and,  in 
consequence  of  which,  is  termed  latent  or  concealed 
heat ;  the  only  positive  proof  we  have  of  its  existence 
beino-  that  of  incontestable  results,  or  effects  produced 
on  various  bodies.  Thus,  if  one  part,  by  weight  of 
steam  at  212°,  be  mixed  with  nine  parts  of  water  at 
62°,  the  result  is  water  at  1/H>°;  therefore,  each  of  thi> 
9  parts  of  water  has  received  from  the  steam  1KH>°  of 
heat  and  consequently,  the  steam  has  diffused,  or  given 
out,  1  HHi  X  9  =  104<>4  —  334  ==  1016°  of  heat,  which 
it  must  have  contained. 

Ao-ain;  it  is  ascertained,  by  experiment,  that  it  one 
<rallo~n  of  water  be  transformed  into  steam  at  212J,  and 
that  allowed  to  mix  with  water  at  52°, the  whole  will  be 
raised  to  the  boilinsr  point,  or  212°.  From  these  and  othej 
experiments  it  ia  ascertained  that  the  latent  heat  in 
steam  varies  from  940°  to  1044s  the  ratio  of  accumula- 
tion advancing  from  212°,  as  the  steam  becomes  more 
dense  and  of  greater  elastic  force.  Hence,  the  severity 
of  a  scald  by  steam  to  that  of  boiling  water. 

Water  holding  impurities  in  solution  tends  to  retard 
its  attaining  the  aeriform  state,  and  so  impairs  the 
amount  of  its  elastic  force  at  an  equal  temperature,  a* 


PROPERTIES    OF    STEAM. 


exhibited   in   the    following  tables, 
water  boils  at  212°  Fahrenheit. 


Thus,   common 


Name  of  substance. 

Pr( 
1 

portionate  quantity  in 
100  parts 
ly  weight  of  water. 

Boiling 
points. 

Salts  in  sea  water. 

3-03. 

213-2°  P 

Sulphnt6  of  soda.  

h 

31-5 

213 

Sulphate  of  iron  .  .      .  . 

64 

°16 

Alum             .            .  .      . 

> 

52 

220 

Sulphate  of  limp              . 

C 

45 

2°0 

Sulphate  of  magnesia  .  . 

mini 

57-5 
30 

222 
224 

Nitrate  of  soda  

8 

60 

246 

Acetate  of  soda    

e 

60 

256 

Elastic  Force  of  Steam  in  Inches  of  Mercury. 

Common  water  )  boiling  point,  212°  F.  (  elastic  force,  30       in 
Sea  water  .  .  .    $  at  212    «   ?  «  23-05  « 

Common  water  )  boiling  point,  216°  F.  (  elastic  force,  32-5    in, 
Sea  water  .  .  .    $  at  216    "  ^  «  24-6     " 

Common  water  )  boiling  point,  220°  F.  (  elastic  force,  35-1    in 
Sea  water ...   5  at  220    "  ?  "  26-5     " 

Hence  the  propriety  of  procuring,  for  steam,  water  in 
its  purest  state. 

Effects  produced  by  Air  in  its  natural  and  also  in  a 
rarefied  State. 

The  weight  or  pressure  of  the  atmosphere  is  equal  to 
the  weight  of  a  column  of  water  34  feet  in  hei"ht,  or  to 
a  column  of  mercury  30  inches  in  height,  or  to  14-7  Ibs. 
a,verage  per  square  inch,  at  a  mean  temperature.  But 
air,  like  all  other  gases,  is  rendered  lighter  by  the  ap- 
plication of  heat ;  for  then  the  particles  of  the  mass  are 
repelled  from  each  other,  or  rarefied,  and  occupy  a 
greater  space.  Rarefied  air,  being  specifically  lio-htest, 
mounts  above  that  of  common  density;  hence  change 
of  temperature,  and  the  principal  cause  of  winds. 


94 


PROPERTIES    OF   AIL. 


Table  of  the  Expansion  of  Atmospheric  Mr  by  Heat. 


Degrees  of 
,  Fahrenheit. 

Bulk. 

Degrees  of 
Fahrenheit. 

Bulk. 

Degrees  of 
Fahrenheit. 

Bulk, 

32° 

1000 

65° 

1077 

100° 

1152 

1       35 

1007 

70 

1089 

120 

1194 

40 

1021 

75 

1099 

140 

1235 

!       45 

1032 

80 

1110 

160 

1275 

50 

1043 

85 

1121 

180 

1315 

*       55 

1055 

90 

1132 

200 

1364 

j       60 

1066 

95 

1142 

212 

1376 

The  pressure  or  gravity  of  the  atmosphere,  being 
equal  to  a  column  of  water  34  feet  in  height,  is  the 
means  or  principle  on  which  rests  the  utility  of  the 
common  pump,  also  of  the  syphon  and  all  other  such 
hydraulic  applications.  In  a  pump,  the  internal  pres- 
sure on  the  surface  of  the  liquid  is  removed  by  the 
iction  of  the  bucket;  and  as  by  degrees  the  density 
becomes  lessened,  so  the  water  rises  by  the  external 
pressure  to  the  abovo-nanied  height;  and  at  such 
leight  it  will  remain,  urJess,  by  some  derangement  of 
construction  taking  place,  the  atmospheric  fluid  is 
allowed  to  enter  and  displace  the  liquid  column.  But 
observe,  if  the  temperature  of  the  water  or  other  liquid 
be  so  elevated  that  steam  01  vapor  arise  through  it, 
ehen,  according  to  tLo  vapcA  accumulation  of  density, 
may  the  action  ol  the  purr»p  be  partially  or  wholly 
destroyed;  and  the  oh'vmepns  >f  evasion  in  such  cases 
>«,  to  place  the  working  W*k*<  beneath  the  surface  of 
^ho  K;u:u  wu:ch  s  tequ;rt>j  <  *>e  raised. 


PTJMPS. 


95 


Table  slmving  the  Quantity  of  Water  per  Lineal  Foot  in 
Pumps,  or  Vertical  Pipes  of  different  Diameters. 


Diameter 
of  pump 
in  inches. 

Number  of 
gallons  per 
lineal  ft. 

Number  of 
cubic  feet 
per  lin.  ft. 

Diameter 
of  pump 
in  inches. 

Number  of 
gallons  per 
lineal  ft. 

Number  of 
cubic  feet 
per  lin  ft. 

2 

•136 

•0218 

8 

2  176 

•3490 

2* 

•172 

•0276 

8£ 

2314 

•3712 

2£ 

•212 

•0340 

8| 

2-456 

•31140 

21 

•257 

•0412 

8| 

2-603 

•4175 

3 

•306 

•0490 

9 

2754 

•4417 

3| 

•359 

•0576 

9i 

2-909 

•4666 

34 

•416 

•0668 

9^ 

3-068 

•41*23 

31 

•478 

•0766 

91 

3-232 

•5184 

4 

•544 

•0872 

10 

3-400 

•5454 

ii 

•614 

•688 

•0985 
•1104 

104 

3-572 

3-748 

5730 
•6013 

41 

•767 

•1230 

10| 

3-929 

•6302 

5 

•850 

•1363 

11 

4-114 

•6599 

5| 

•937 

•1503 

111 

4-303 

6902 

5^ 

1-028 

•1649 

Hi 

4-496 

•7212 

5| 

1-124 

•1803 

llf 

4-694 

»7529 

6 

1-224 

•1963 

12 

4-896 

•7853 

DT 

1-328 

•2130 

I2i 

5-312 

•8521 

el 

1-436 

•2304 

13 

5746 

•9217 

1-549 

•2489 

13£ 

6196 

•9939 

7 

1-666 

•2672 

14 

6664 

1-0689 

74 

1-787 

•2866 

15 

7-650 

12271 

g 

1-912 

•3067 

16 

8-704 

1-3962 

1 

2-042 

•3275 

18 

11-016 

17670 

Examples  illustrative  of  the  Utility  of  the  Table. 

1.  Required  the  quantity  of  water  lifted  by  each 
Btroke  of  the  bucket  of  a  9£  -inch  pump,  the  length  of 
the  stroke  being  2|  feet 

3-068  X  2-25  =  6-903  gallons,  each  stroke. 

2.  What  length  of  stroke  with  a  6-inch  pump  will 
De  necessary,  to  discharge  44  gallons  of  water  per 

9 


B6  PROPERTIES    OF    AIR. 

minute,  the  number  of  strokes  being  18  in  the  given 
time? 

44 

=  2  feet,  the  length  of  stroke. 

1-224  X  18 

3.  What  must  be  the  diameter  capable  of  raising 
25  cubic  feet  of  water  per  minute,  the  length  of  the 
stroke  being  2£  feet,  and  making  16  effective  strokes 
per  minute  ? 

25 

==  -625,  or  105  inches,  nearly. 

2-5  x  16 

It  is  by  the  oxygen  of  the  atmosphere  that  com- 
bustion is  supported.  The  common  combustibles  of 
nature  are  chiefly  compounds  of  carbon  and  hydrogen, 
which,  during  combustion,  combine  with  the  oxygen 
of  the  atmosphere,  and  are  converted  into  carbonic 
acid  and  watery  vapor,  different  species  of  fuel  re- 
quiring different  quantities  of  oxygen.  The  quantity 
required  for  the  combustion  of  a  pound  of  coal  varies 
from  2  to  3  Ibs.,  according  to  the  quality  of  the  coal. 
60  cubic  feet  of  atmospheric  air  is  necessary,  to  pro- 
duce 1  Ib.  of  oxygen. 

The  pressure  or  fluid  properties  of  the  atmosphere 
oppose  bodies  in  passing  through  it,  the  opposing  re- 
sistance increasing  as  the  square  of  the  velocity  of  the 
body,  and  the  resistance  per  square  foot  in  Ibs.  as  its 
velocity  in  feet  per  second,  multiplied  into  -002288. 
Thus,  suppose  a  locomotive  engine  in  a  still  atmosphere, 
at  a  velocity  of  25  miles  per  hour,  presents  a  resisting 
frontage  of  20  feet ;  required  the  amount  of  opposing 
resistance  at  that  velocity. 

25  miles  per  hour  equal  3fr67  feet  per  second. 
Then   36-672  x  -002288  x  20  =  61-5  Ibs.,   constant  opposing 
force 


WINDS. 


97 


Table  of  the   Force  and  common  Appellations  given  /o 
Winds  at  different  Velocities. 


Velocity  of  the  Wind  in 

Force  in  Ihs. 
avoirdupois 
per  square 
foot. 

Common  Appellations 
given  to  the  Wind. 

Miles  per 
hour. 

Feet  per 
second. 

1 

1  47 

•005 

Hardly  perceptible. 

2 
3 

2-!  13 
440 

•020 
•044 

Just  perceptible. 

4 
5 

5  87 
7-33 

•079 
•123 

Gentle,  pleasant  wind. 

10 
15 

1467 
22-00 

•492 
1  107 

>  Pleasant,  brisk  gale. 

20 
25 

2!  134 
3H67 

1  968 
3075 

>  Very  brisk. 

30 
35 

4401 
51  34 

4-42!) 
6(i27 

>  High  winds. 

40 
45 

58-68 
6601 

7873 
9-963 

>  Very  high. 

50 

73  35 

12-300 

A  storm  or  tempest. 

60 

8802 

17715 

A  oreat  storm. 

80 

117-36 

31  490 

A  hurricane. 

Ill  order  to  gain  the  greatest  amount  of  the  wind's 
impulsive  effect,  to  produce  rotary  or  circular  motion  by 
the  sails  of  a  wind- mill,  the  total  surface  of  the  sails 
presented  to  the  wind  ought  to  be  about  seven-eighths 
of  ihe  circle's  surface  which  is  formed  by  their  motion, 
and  each  sail  angled  to  the  plane  of  motion  as  follows, 
the  whip  or  back  being  divided  into  six  equal  parts:  — 

Distance  from  centre  of  motion,  1      2345     6  )  Smeaton'i 
>.ngle  with  plane  of  motion,       18°  19  18  16  l°2£   7  $       rule. 
%  G.  Forrester,  Liverpool,       24°  21  18  14   9     3 


FRICTION. 


FRICTION. 

FRICTION  is  an  effect  produced  by  bodies  rubbing 
one  upon  another,  which  acts  as  a  retarding  influence 
in  the  motion  of  all  mechanical  contrivances,  hut 
might  not  unfrequently  be  considerably  diminished  by 
a  due  regard  to  its  laws,  and  a  proper  attention  to 
the  selection  of  those  materials  on  which  a  uniform 
smooth  surface  may  he  attained,  and  which,  according 
to  experiments,  are  least  liable  to  tear  or  become  hot, 
and  cause  a  roughness  to  arise  when  in  working 
contact 

Several  doubts  existed,  until  lately,  respecting  the 
laws  of  friction ;  but  those  are  now  entirely  removed, 
through  the  experiments  of  Mr.  G.  Rennie,  on  his  own 
account,  and  those  of  M.  Morin,  acting  for,  and  under 
the  sanction  of,  the  French  government,  from  or  by 
which  the  following  laws  have  been  fully  established :  — 

1.  The  friction  accompanying  the   motion  of  two 
surfaces,   between   which   no  unguent  is  interposed, 
bears  the  same  proportion  to  the  force  by  which  those 
surfaces  are  pressed  together,  whatever  may  be  the 
amount  of  that  force. 

2.  This  friction  is  independent  of  the  extent  of  the 
surfaces  of  contact. 

3.  Where  unguents  are  interposed,  a  distinction  is 
to  be  made  between  the  case  in  which  the  surfaces  are 
simply   unctuous   and   in   intimate   contact  with  one 
another,  and  the  case  in  which  the  surfaces  are  wholly 
separated  from  one  another  by  an  interposed  stratum 
of  the  unguent.     If  the   pressure   upon  a  surface  of 
contact  of  given  dimensions  be  increased  beyond  a 
certain  limit,  the  latter  of  these  cases  passes  into  the 
first;  the  stratum  of  unguent  being  pressed  out,  and 
the  unctuous  surfaces,  which  it  separated  from  one 


FRICTION.  99 

another,  being:  brought  into  intimate  contact.  As  long 
as  either  of  these  two  states  remain,  the  laws  of  its 
friction  are  not  affected  by  the  presence  of  the  unguent : 
but,  in  the  transition  from  the  one  state  to  the  other,  an 
exception  is  made  to  the  independence  of  the  friction 
upon  the  extent  of  the  surface  of  contact;  for,  sup- 
posing the  extent  of  two  surfaces  of  contact,  between 
which  a  stratum  of  unguent  is  interposed,  and  which 
sustain  a  given  pressure,  to  be  continually  diminished, 
it  is  evident,  that  the  portions  of  this  pressure  which 
take  effect  upon  each  element  of  the  surfaces  of  con- 
tact will  be  continually  increased,  and  that  they  may 
thus  be  so  increased  as  to  press  out  the  interposed 
stratum  of  unguent,  and  cause  the  state  of  the  surfaces 
to  pass  into  that  which  is  designated  as  unctuous, 
thereby  changing  the  coerficient  of  friction.  That 
law  of  friction,  then,  which  is  known  as  the  law  of  :  : 
the  independence  of  the  surface,  is  to  be  received,  in 
the  case  where  a  stratum  of  unguents  is  interposed, 
only  within  certain  limits. 

It  will  be  understood,  from  what  has  been  said,  that 
there  are  three  states,  in  respect  to  friction,  into  which 
the  surfaces  of  bodies  in  contact  may  be  made  suc- 
cessively to  pass :  one,  a  state  in  which  no  unguent  is 
present;  the  second,  a  state  in  which  the  surfaces  are 
unctuous,  but  intimately  in  contact;  the  third,  a  state 
in  which  the  surfaces  are  separated  by  an  entire 
stratum  of  the  interposed  unguent. 

Throughout  each  of  these  states,  the  coefficient  ot 
friction  is  the  same;  but  it  is  essentially  different  in 
the  different  states. 

4.  It  is  a  law  common  to  the  friction  of  all  the 
states  of  contact  of  two  surfaces,  that  their  friction, 
when  in  motion,  is  altogether  independent  of  the 
velocity  of  the  motion.  M  Morin  has  verified  this 
law,  as  well  in  various  st  >tes  of  contact  without  inter- 
oosed  fluids,  as  in  the  cases  where  water,  oils,  grease, 
glutinous  liquids,  sirups,  pitch,  were  interposed  in  fc 
continuous  stratum. 
9* 


100  BOILERS. 

The  variety  of  the  circumstances  under  which  these 
laws  obtain  in  respect  to  the  friction  of  motion,  and 
the  accuracj?  with  which  the  phenomena  of  motion 
accord  with  them,  may  be  judged  of  from  one  example, 
taken  from  the  first  set  of  experiments  of  M.  Morin 
upon  the  friction  of  surfaces  of  oak,  whose  fibres  were 
parallel  to  the  direction  of  their  motion  upon  one 
another.  He  caused  the  surfaces  of  contact  to  vary 
their  dimensions  in  the  ratio  of  1  to  84,  —  from  less 
than  5  square  inches  to  nearly  3  feet  square;  the 
forces  which  pressed  them  together  he  varied  from 
88  Ibs.  to  2205  Ibs.,  and  their  velocities  from  the  slow- 
est possible  to  9-8  feet  per  second,  —  causing  them  to 
be  at  one  period  accelerated  motions,  at  another  uni- 
form, at  a  third  retarded ;  yet,  through  all  this  wide 
range  of  variation,  he  in  no  instance  found  the  co- 
efficient of  friction  to  deviate  from  the  same  fraction 
of  0-478  by  more  than  ^V  of  the  amount  of  the 
fraction. 


RULES,   TABLES,  ETC.,  RELATIVE   TO 
BOILERS  AND  THE  STEAM-ENGINE. 

THE  boiler  of  a  steam-engine  may  be  explained  as 
that  portion  of  the  structure  in  which  the  vital  prin- 
ciple of  the  engine  is  generated;  consequently,  its 
construction  is  of  the  utmost  importance  ;  for  upon  the 
proper  efficiency  of  the  boiler  depends,  in  a  great 
measure,  the  efficiency  of  the  engine. 

Boilers  not  unfrequently,  because  of  unavoidable 
peculiarities,  are  necessarily  constructed  of  various 
forms ;  but,  for  land  or  stationary  engine  boilers,  if  no 
thwarting  circumstances  intervene,*  either  the  wagon 
or  cylindrical  forms  are  commonly  resorted  to;  the 


BOILERS.  101 

former  for  those  of  condensing  engines,  and  the  latter 
for  those  of  the  high-pressure  principle. 

In  the  construction  of  boilers,  much  attention  ought 
to  be  paid  in  avoiding  thin  films  of  water  where  the 
action  of  the  fire  is  great ;  because  it  is  neither  con- 
sistent with  safety,  nor  can  there  be  the  proper  quan- 
tities of  steam  generated,  according  to  the  surface 
exposed,  unless  under  some  extraordinary  degree  of 
pressure.  Also,  convex  surfaces,  exposed  to  the  action 
of  the  steam,  unless  properly  supported,  ought  strenu- 
ously to  be  avoided.  Large  water  spaces,  concave 
surfaces,  or  straight  plates  securely  stayed,  with  ample 
steam-room,  are  the  chief  requisites  to  l*°  attended  to. 

1.  To  determine  the  proper  quantity  of  heating  sur- 
face in  a  boiler  for  an  engine  with  a  cylinder  of  a  given 
capacity,  and  steam  at  any  density  required. 

Rule.  —  Multiply  375  times  the  area  of  the  cylinder 
in  feet  by  the  velocity  of  the  piston  in  feet  per  minute, 
and  divide  the  product  by  the  volume  of  steam  to  1  of 
water  at  the  density  required,  (see  Table,  page  91 ;) 
and  the  quotient  is  the  amount  of  effective  heating 
surface  in  square  feet. 

Ex.  Required  the  amount  of  effective  heating  sur- 
face in  a  boiler  for  an  engine  whose  cylinder  is  4£ 
square  feet  in  area,  and  the  piston's  velocity  !224  feet 
per  minute,  the  pressure  of  the  steam  to  eq'ual  5  Ibs. 
per  square  inch  above  the  pressure  of  the  atmosphere. 

375  x  4-5  X  224 

=  295  square  feet;  nearly ;  the  fire-grate  be- 
ing in  accordance  with  the  following  rule. 

Multiply  the  number  of  square  feet  of  heating  sur- 
face by  -12,  the  product  equal  the  area  of  fire-grate  in 
square  feet,  thus  :  — 

295  X  -12  =  354  square  feet  of  furnace  bar. 

Note.  —  By  effective  heating  surface  is  meant  horizontal  sur- 
faces over  fire,  flame,  or  heated  air;  vertical  or  side  surfaces 
requiring  about  If  feet  to  equal  in  effect  1  of  hori/ontal  su»-fai  *. 


102 

2.  To  determine  the  proper  dimensions  for  a  loagon- 
•haped  boiler,  when  the  amount  of  effective  heating  sur- 
face in  square  fed  is  obtained  by  the  preceding  ride. 

1.  The  bottom  surface  equal  half  the  whole  surface 

2.  The  length  of  the  boiler  equal  twice  the  square 
root  of  bottom  surface. 

3-   The  width  equal  one-fourth  the  length ;  and 
4.   The  height  equal  one-third  the  length. 

Ex.  Roquired  the  dimensions  for  a  boiler  of  the 
wagon  form,  that  may  present  an  effective  heating  sui- 
face  of  295  square  feet. 

Bottom  surface  =295  —  2,  or  147-5  square  feet 
Length  .     .     .    =  V14r5  x  2,  or  24-26  feet. 
Width    .     .     .   =  24-2fi  —  4,  or  fi-Ofi  foot. 
Height.    .    .   =24-264-3,  or  8-08  feet. 

Note. — The  amount  of  side  or  vertical  surface  equal  twice 
the  length  of  the  boiler,  added  to  the  width,  and  multiplied  \*j 
•75  to  obtain  that  of  effective  surface  j  hence, 

147-5  x  1-75 

-  =  4-7  feet,  depth  of  side  flue. 


24-26  x  2  +  G-06 


3.  To  determine  the  dimensions  for  a  cylindrical 
boiler. 

Ru'e.  —  Extract  the  square  root  of  1  34  times  the 
effective  heating  surface  in  square  feet,  and  twice  the 
root  equal  the  builer's  circumference  in  feet;  also,  the 
circumference  equal  the  length. 

E.r.  Let  a  cylindrical  boiler  be  required  with  ai 
effective  heating  surface  of  8<>  square  feet;  what  mus 
be  its  length  and  diameter  in  feet? 

y8G  X  1-31=  10-71  X  2  =  21-48  foot   circumference,  or  b 
feet  10   nches  diameter,  and  21-48  feet  in  length. 

Note.  —  When  an  internal  flue  is  to  be  insrrtod  in  a  boilei 
tie  external  surface  of  the  boiler  may  be  diminished  in  lengtf< 


BOILERS.  lUft 

equal  to  half  the  exposed  surface  of  the  flue.  Observe,  also, 
that  the  height  of  the  contained  water  in  boilers  generally 
ought  to  be  about  two-thirds  the  whole  height  of  the  boiler 


Specified  Particulars  relative  to  the  Boiler  and  Engine, 

Diameter  of  cylinders, 14  inches. 

Length  of  stroke,       18      •< 

T^ap  of  the  valve, 1    inch. 

Diameter  of  driving  wheels, 5^  feet. 

Length  of  internal  fire-box,     .     .     .   2  feet  llj  inches. 

Width  of  do., 3    "      5        " 

Length  of  cylindrical  part  of  boiler,  8     "      8        " 

Diameter  of  do., 3    "      4A      " 

Length  of  tubes, .    8    "    11 J      « 

Number  of  tubes,       ......    133,  of  brass. 

Interior  diameter  of  do., 1^  inches. 

Diameter  of  blast-pipe, 4        " 

About  112  Ibs.  of  coke,  consumed  in  this  boiler 
evaporate  84  gallons  of  water ;  and  from  30  to  25  Ibs 
of  coke  are  consumed  per  mile. 


Heating  Powers  of  Combustible  Substances 


Species  of  combustible.  ' 

Ibs.  of 
water 
heated 
from  32° 
to  212°. 

Ibs.  of  boil- 
ing water 
evaporated 
by  1  lb.  of 
fuel. 

Ibs.  of 
atmospheric 
air  to  each 
lb.  of  fuel. 

Wood  in  its  ordinary  state 
Wood  charcoal  

26 
73 

4-72 
13-37 

4-47 
11-46 

Coal      

60 

10-90 

9-26 

Coke  

65 

11-81 

11-46 

Turf  

30 

5-45 

4-60 

L  Tnrf  charcoal     

64 

11-63 

9-86 

104 


STEAM-ENGINES. 


Table  of  Dimensions  for  Steam- Engine  Cylinders  by 
celebrated  Makers. 


Sin  l  OIIKFV  Con- 
deiMiif  £,*„„.«, 
y  B-iilioii  &  Wat 


'  ' 


f) 

8 
10 
12 
14 
1(5 
18 
i  20 

24 

25 
2fi 

28 
30 
3.0 
40 

50 

r.o 


i! 


Marine  Engine., 
by  iM;ui.Uley, 
Napier,  &c. 


10 

15 

20 
25 
30 
40 
50 

70 

80 

90 
100 
110 
120 
130 
150 
200 
250 i  84 


20 

24 
27 

32 
3fJ 
40 
43 


If 


Hitrh  Pressure,  or 

Non-Conilfiisin?  Kr.g-inet, 

by  vurioiis  makers. 


FMameters  of  cylinders, 

the  torce  ol  (.he  •team  being, 

per  square  inch, 


25  Ibs.    30  Ibs.    40  1U.    5u 


?f 


15 


The  ?m?7  of  nominal  power  for  steam-engines,  or  the 
usual  estimate  of  dynamical  effect  per  minute  of  a 
horse,  called,  hy  engineers,  a  horse-powrr,  is  33,000  Ibs., 
at  a  velocity  of  1  foot  per  minute;  or,  the  effect  of  a 
load  of  2i.O  Ibs.,  raised  by  a  horse,  for  8  hours  a  day, 
at  the  rate  of  '<>£  miles  per  hour,  or  150  Ibs.  at  the  rate 
of  l&JO  feet  per  minute 


TROi^KKTlhS    OF    BODIES. 


10.5 


ip"!-H  qsruo 
upithu  euoj. 


•  —  <M  a  G*  OJ 


Illllllllilllll 


gi   \™*>  I    |&     I    ob     I    S  I      I    1^ 


|OQ  |<oe«  |    |~     |      |      |    rr 


•  qp    i  o  -y  o    ,  o)  s  Si  I    s  ?t^    I    -  3.CJ  «p 
l«   1— oioi    '<Mc^    '    cJ;T    '    z  *• 


)  piny  a;ji  ujoj)  jooj 
nauj|  jaJqaui'irajo 
uvd  ui  uouaiuniof) 


MJ  siuiod  gupp 


jAtuS  Dgpadg 


sooo 


-2 


CJ    f^  x    cc    §1  — 
t*    r»t—   r»   i-»r^ 


106 


PROPERTIES    OF    BODIES. 


WOODS 

Names. 

ll 
of 

{! 

c 

u 
IS 

3 

0 

Ultimate  coh"- 
»ivo  strength  "f 
an  inch  squire 
prism  in  Ibs. 

Ct.  in  par  alive 

Stiffness. 

Strength. 

0 

i 

934 
872 
756 
672 
852 
800 
640 
604 
610 
845 
673 
800 
637 
671 
750 
640 
944 
383 
561 
753 
546 
528 
590 
551 
461 
660 
530 
240 

58 
54 
47 
42 
48 
46 
40 
38 
38 
52 
42 
50 
40 
42 
46 
40 
59 
34 
33 
47 
34 
33 
37 
34 
28 
41 
31 
15 

48 
53 
45 
48* 
55 
59 
59 
43 
53 
45 
55 
53 
484 
55 
38 
66 
68 
48 
66 
68 
60 
66 
80 

149 

11880 
12888 
12780 
10253 
12225 
9540 
10935 
9630 
10656 
14130 
9720 
7560 
11475 
8800 
12915 
12350 
17200 
5928 
7420 
9540 
9540 
7110 
12346 
10296 
11853 
9796 
12240 

100 
93 
117 
114 
77 
63 
78 
59 
67 
89 
78 
73 
93 
49 
126 
99 
101 
44 
28 
98 
114 
55 
104 
72 
95 
73 
79 

100 
108 
107 
86 
103 
80 
92 
81 
89 
119 
82 
67 
96 
74 
109 
104 
144 
50 
62 
80 
80 
60 
104 
86 
99 
82 
103 

100 
125 
99 
64 
138 
101 

111 
118 
lf.0 
86 
61 
99 
111 
94 
82 
138 
57 
106 
64 
56 
65 
104 
102 
103 
92 
134 

Darvtzic  do  

Beech   

\lder  

Chestnut  

Ash   

Mahogany,  Spanish  . 
"     Honduras 
Walnut  

Teak  

Cedar  

Riga  fir     .... 

Christ.  Wht.  deal  .  .  . 
Amern.  white  spruce  . 

Cork  

J 

PROPERTIED    OF    BOLILS. 

1U7 

LIQUIDS. 

GASES. 

x 

_  c 

Atmospheric    air    being    the 

'>  g 

K~ 

standard  of  cumparis 

en, 

I" 

*S  ««--rf 

or  1000. 

Names. 

If 

"£1-0  s 

c  •'*• 

|l 

UQ 

*t 

Names. 

l! 

Acid,  sulphuric 
"      nitric     .  . 

1850 
1271 

18-5 
12-7 

Hydriodic  acid  gas 
Chlorine       "       " 

4340 
25fO 

"      muriatic  . 

1200 

12-0 

Carbonic      "       " 

1527 

1 

"      fluoric  .  . 

1060 

10-6 

JVitrous  oxide      " 

1527 

"      citric     .  . 

1034 

10-3 

Cvariogen            " 

1805 

| 

"      acetic   .  . 

1062 

10-6 

Oxygen               " 

nil 

Water  from  the 

Carbonic  oxide  " 

972 

Baltic  

1015 

10-2 

Water  from  the 

drotren        ^"  u 

972 

Dead  Sea  .  .  . 

1240 

12-4 

Prussic  acid        " 

937 

Water  from  the 

Amrnoniacal        " 

590 

Mediterranean 

1029 

10-3 

Steain  of  water  " 

623 

Water,  distilled 

1000 

IOO 

Hydrogen            '» 

69 

; 

Oils,  ex  pressed  : 
linseed  .... 

940 

9-4 

Weijiht    of    water    at    the 

sweet  almond 

932 

9-3 

common  temperature  : 

whale    .... 

923 

9-2 

1  cubic  ln.=     -aW/  Ib. 

; 

' 

hempseed  .  . 
olive         .  .  . 

926 
915 

9-3 
9-2 

1  '  "     ft,  —  (52-5  Ihs. 
1      "     «»  =  6-2/i  imp.  galls. 

, 

Oils,  essential  : 
cinnamon  .  . 
lavender  .  .  . 
tuq>entme  .  . 

1043 
894 
870 

10-4 
8-9 
8-7 

1-8  "     "   =    1  rwt. 
1  cylin.  Jn.=     -(h>842  Ib. 
1      "     ft.  =4P-I  Ibs. 
1      "      "   =  5  imp.  galls. 
2-282  feet    =    1  cwt. 

i 

amber    .... 

8(58 

87 

11-2  imp.  galls.  =  1  cwt. 

825 

8-2 

224      »        »     =rlton. 

Kther,  nitric  .  . 

908 

9-1 

Proof  spirit  .  . 
Vinegar  

922 
1009 

9-2 
10-1 

10 

V 

PRACTICAL    1ABLES.  109 


PRACTICAL   TABLES, 


WEIGHT  OF  METALS. 


WROUGHT    IRON  J     SQUARE,    ROUND,    AND    FLAT. 

Table  I.  contains  the  weight  of  Square  Iron  in  sizes, 
from  4  inch  to  six  inches  square,  advancing  by  £  inch ; 
and  from  6  to  12  inches  square,  advancing  by  |  inch ; 
and  in  lengths,  from  1  foot  to  18  feet  The  sizes  are 
arranged  in  the  first  column  of  each  page,  and  the 
lengths  along  the  top ;  the  weight  in  Ibs.  immediately 
under  the  lengths,  and  in  a  line  with  the  sizes. 

Table  II.  contains  the  weight  of  Round  Iron  in  sizes 
from  \  inch  to  6  inches  diameter,  advancing  by  J  inch ; 
and  from  6  to  12  inches  diameter,  advancing  by  |  inch ; 
and  in  lengths  from  1  foot  to  18  feet.  The  sizes, 
lengths,  and  weights  are  arranged  as  in  Table  I. 

Table  III.  contains  the  weight  of  Flat  Iron  in 
widths,  from  |  inch  to  6  inches  diameter,  advancing  by 
|  inch  ;  in  thicknesses  from  £  inch  to  1  inch,  advancing 
by  \  inch ;  and  in  lengths,  from  1  to  18  feet  The 
widths,  lengths,  and  weights,  are  arranged  as  in  the 
preceding  tables,  and  the  thicknesses  alongside  of  tha 
widths, 


110  PRACTICAL    TABLES. 

TABLE    I  —  SaUARE    IRON. 


size. 

( 

Itt 

*«. 

3ft. 

* 

5ft. 

Gft. 

7ft. 

8ft     9ft. 

inch. 

\s. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

His. 

Ibs. 

Ibn 

^ 

0-2 

04 

0-6 

0-8 

1-1 

13 

1-5 

1-7 

19 

I 

0-5 

10 

1  4 

1-9 

2-4 

2-9 

3-3 

3-8 

4-3 

i 

0-8 

17 

2-5 

3-4 

4-2 

5-J 

5-9 

68 

7-6 

1 

1-3 

2-6 

4-0 

5-3 

6-6 

7-9 

9-2 

10-6 

11-9 

1 

1-9 

3-8 

5-7 

7-6 

9-5 

11-4 

13-3 

15-2 

17-1 

I 

2-6 

5-2 

7-8 

10-4 

12-9 

15-5 

18-1 

20-7 

23-3 

1 

3-4 

6-8 

10-1 

13-5 

16-9 

20-3 

23-7 

27-0 

30-4 

1! 

4-3 

8-6 

12*8 

17-1 

21-4 

25-7 

29-9 

34-2 

38-5 

14 

5-3 

10-6 

15-8 

21-1 

26-4 

31-7 

37-0 

42-2 

47-5 

M 

6-4 

12-8 

19-2 

25-6 

32-0 

38-3 

44-7 

51-1 

57-5 

i._i 

7-6 

15-2 

22-8 

30-4 

38-0 

45-6 

53-2 

6)-8 

68-4 

ii 

8-9 

17-9 

2(5-8 

3>7 

44-6 

53-6 

62-5 

71-4 

80-3 

15 

10-4 

20-7 

31-1 

41-4 

51-8 

62-1 

72-5 

82-8 

93-2 

ii 

11-9 

23-8 

35-6 

47-5 

59-4 

71-3 

83-2 

95-1 

10G-9 

2 

13-5 

27-0 

40-6 

54-1 

67-6 

81-1 

94-6 

108-2 

121-7 

2£ 

15-3 

30-5 

45-8 

61-1 

76-3 

91-6 

106-8 

122-1 

137-4 

24 

17  1  !     34-2 

51-3 

68-4 

85-6 

102-7 

119-8 

136-9 

154-0 

21 

19-1 

38-1 

57-2 

76-3 

95-3 

114-4 

133-5 

15Q-5 

171-6 

2£ 

21-1 

42-2 

63-4 

84-5 

105-6 

126-7 

147-8 

169-0 

190-1 

2  1 

23-:< 

4(;-6 

69-9 

93-2 

116-5 

139-8 

163-0 

186-3 

209-6 

2^ 

25-6 

51-1 

767 

102-2 

127-8 

153-4 

178-9 

204-5 

230-0 

28 

27-9 

55-9 

83-8 

111-8 

139-7 

1676 

195-7 

223-5 

251-5 

3 

30-4 

60-8 

91-2 

121-7 

152-1 

182-5 

212-9 

243-3 

273-7 

3$ 

33-0 

66-0 

99-0 

132-0 

165-1 

198-1 

231-1 

264-1 

297-1 

34 

35-7 

71-4 

107-1 

142-8 

178-5 

214-2 

249-9 

285-6 

321-3 

Jj| 

38-5 

77-0 

115-5 

154-0 

192-5 

231-0 

2C9-5 

308-0 

346-5 

3* 

41-4 

82-8 

124-2;    165-6 

207-0 

248-4 

289-8 

331-3 

372-7 

3| 

44-4 

88-8 

133-3 

17"  -7 

222-1 

266-5 

310-9 

355-3 

,399-8 

33 

47-5 

95-1 

142-6 

190-1 

2377 

285-2 

3327 

380-3 

427-8 

31 

5-8 

10J-5 

'152-3 

203-0 

253-8 

304-5 

355-3 

406-0 

456-8 

fj 

PRACTICAL    TABLES.                             Ill 

TABLE    I.—  SQUARE    IRON. 

size 

10ft 

lift 

12ft 

13ft 

14ft. 

15ft.  16ft. 

17ft. 

18ft 

J 

inch. 

ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

i 

2-1 

2-3 

2-5 

2- 

3- 

3-2 

3- 

3-6 

3-8 

I 

4'8 

5-2 

5-7 

6-2 

6-7 

7-1 

7- 

8-1 

8-6 

i 

8-5 

9-3 

10-1 

11-0 

11-8 

12-0 

13- 

14-4 

15-2 

I 

13-2 

14-5 

15-8 

17-2 

18-5 

19-8 

2J- 

22-4 

23-8 

1 

19-0 

20-9 

22-8 

24-7 

26-6 

28-5 

30-4 

32-3 

34-2 

£ 

25-9 

28-5 

31-1 

33-6 

36-2 

38-8 

41-4 

44-0 

46-6 

i 

33-8 

37-2 

40-6 

43-9 

47-3 

50-7 

54-1 

57-5 

60-8 

i* 

42-8 

47-1 

51-3 

55-6 

59-9 

64-2 

68-4 

72-7 

77-0 

i* 

52-8 

58-1 

63-4 

68-6 

73-9 

79-2 

84-5 

89-8 

95-0 

if 

63-9 

70-3 

76-7 

83-1 

89-5 

95-9 

102-2 

108-6 

115-0 

u 

76-0 

83-6 

91-2 

98-9 

106-5 

114-1 

121-7 

129-3 

136-9 

It 

89-3 

98-2 

107-1 

116-0 

125-0 

133-9 

142-8 

151-7 

160-7 

11 

103-5 

133-9 

124-2 

134-6 

144-9 

155-3 

165-6 

176-0 

186-3 

is 

118-8 

130-7 

142-6 

154-5 

166-4 

178-2 

190-1 

202-0 

213-iJ 

2 

135-2 

148-7 

162-2 

175-8 

189-3 

202-8 

216-3 

229-8 

243-4 

< 

2£ 

152-6 

167-9 

183-2 

198-4 

213-7 

2289 

244-2 

259-5 

274-7 

2i 

171-1 

188-2 

205-3 

222-5 

239-6 

2567 

273-8 

290-9 

308-o) 

2| 

190-7 

209-7 

228-8 

247-9 

266-9 

286-0 

305-1 

324-1 

343-2 

24 

211-2 

232-3 

253-4 

274-6 

295-7 

316-8 

337-9 

359-0 

380-2 

21 

232-9 

256-2 

279-5 

302-8 

326-1 

349-4 

372-7 

396-0 

419-3 

21 

255-6 

281-2 

306-7 

332-3 

357-8 

383-4 

409-0 

434-5 

460-1 

2$ 

279-4 

307-3 

335-3 

363-2 

391-1 

419-1 

447-0 

475-0 

5029 

3 

304-2 

334-6 

365-0 

395-4 

425-8 

456-2 

486-7 

517-1 

547-5 

3J 

330-1 

363-1 

396-1 

429-1 

462-1 

495-2 

528-2 

561-2 

594-2 

3| 

357-0 

392-7 

428-4 

464-2 

499-9 

535-6 

571-3 

607-0 

642-7 

3| 

385-0 

423-5 

462-0 

500-5 

539-0 

577-5 

616-0 

654-6 

693-1 

3£ 

414-1 

455-5 

496-9 

538-3 

579-7 

621-1 

662-5 

703-9 

745-3 

3| 

444-2 

488-6 

533-0 

577-4 

621-9 

666-3 

710-7 

755-1 

799-5 

31 

475-3 

522-9 

570-4 

617-9 

665-5 

713-0 

760-5 

808-1 

855-6 

3} 

507-6 

558-3 

609-1 

659-8 

710-6 

761-3 

812-1 

862-9 

913-6 

10* 

B 

PRACTICAL    TABLES. 
TABLE    I.  — SQUARE    IRON. 


size. 

1ft. 

aft.  |m 

4ft. 

5ft. 

Gft. 

7ft 

8ft 

9ft 

inch 

Ibs. 

Ibs. 

Ibs. 

!bs. 

Ibs. 

11.9. 

Ibs. 

11)9. 

Ibs. 

4 

54-1 

108-2 

162-3 

216-3 

270-4 

324-5 

378-6 

432-7 

486-8 

4& 

57-5 

1  15-0 

172-6 

230-1 

287-6 

345-  1 

41)2-6 

460-1 

517-7 

4<i 

61-1 

122-  1 

183-2 

244-2 

31)5-3 

366-3 

427-4 

488-4 

549-5 

4| 

64-7 

129-4 

11)4-1 

258-8 

323-5 

388-2 

452-9 

517-6 

582-3 

68-4 

136-U 

205-3 

273-8 

342-2 

410-7 

479-1 

547-6 

616-0 

4| 

72-3 

144-6 

216-9 

2H9-2 

361-5 

433-8 

506-1 

578-4 

650-7 

41 

76-3 

152-5 

228-8 

305-1 

381-3 

457-6 

533-8 

610-1 

686-4 

45 

80-3 

160-7 

241-0 

321-3 

401-7 

482-0 

562-3 

642-7 

723-0 

5 

84-5 

169-0 

253-4 

337-9 

422-4 

506-9 

591-4 

675-8 

760-3 

5$ 

88-8 

177-6 

266-4 

355-  1 

443-9 

SJ2-7 

621-5 

710-3 

799-1 

51 

93-2 

186-3 

279-5 

372-7 

465-8 

559-0 

652-2 

745-3 

838-5 

51 

97-7 

195-3 

293-0 

390-6 

488-3 

585-9 

683-6 

781-3 

878-9 

.*>£ 

102-2 

204-5 

306-7 

409-0 

511-2 

613-4 

715-7 

817-9 

920-2 

5| 

107-0 

213-5 

320-9 

427-8 

534-8 

641-7 

748-7 

855-6 

962-6 

51 

111-8 

223-5 

335-3 

447-0 

558-8 

670-5 

782-3 

894-0 

1005-8 

55 

116-7 

233-3 

350-0 

466-7 

583-4 

700-0 

816-7 

933-4 

1050-0 

6 

121-7 

243-3 

365-0 

486-7 

608-3 

730-0 

841-6 

973-3 

1095-0 

*>4 

132-0 

264-1 

396-1 

528-2 

660-2 

792-2 

924-3 

1056-3 

1188-4 

Gd 

142-8 

285-6 

428-4 

571-3 

714-1 

856-9 

999-7 

1142-5 

1285-3 

HI 

154-0 

308-0 

462-0 

616-0 

770-1 

J24-  1 

1078-1 

1232-1 

1386-1 

7V 

165-6 

331-2 

496-9 

662-5 

828-2 

993-8 

1159-4 

1325-1 

1490-7 

7| 

177-7 

355-3 

533-0 

710-7 

888-4 

K)66-o|  1243-7!  1421-4  1599-0 

71 

190-1 

380-3 

570-4 

760-5 

950-7 

1J4H-8',  1331-0 

1521  ;  1711-2 

71 

2J3-0 

406-0 

609-1 

812-1 

1015-1 

1218-1 

1421-2 

1621-2 

1827-2 

8 

216-3 

432-7 

649-0 

865-3 

1081-7 

1298-0 

1514-4 

1730-7 

{U47-0 

84 

23>1 

460-1 

»:s»2 

92'  1-3 

1150-3 

1380-4 

1J10-5 

1840-5'  -2  >70-0 

8i 

241-2 

488-4 

732-7 

976-9 

1221-1 

1465-3  1709-5 

1953-8  'ai  118-u 

81 

258-8 

517-6 

776-4 

10:15-2 

1294-0 

1552-8 

1811-6 

2070-4 

2329-2 

9 

273-8 

|  547-6 

«1H 

1095-2 

I3C9-0 

1642-8 

19U>-5 

2190-3 

2464-1 

PRACTICAL    TABLES. 
TABLE    I.  — SaUARE    IRON. 


size.'  10  ft  lift.  12  ft.1  13  ft 

14ft  lot1. 

1<>  ft 

17ft. 

18ft 

inch. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

4 

540-8 

594-9 

649-0 

703- 

757-2 

811-3 

8G5-; 

919-4 

973-5 

575-2 

632-7 

693-2 

747-7 

805-2    862-8    920-3 

977-8  1035-3 

44 

610-6 

671-6 

732-7 

793-7 

854-8    915-8 

976-9 

1037-9 

1099-0 

41 

646-0 

711-7 

776-4 

841-1 

905-8 

970-5 

1035-2 

1099-9 

1164-6 

41 

684-5 

752-9 

821-4 

889-8 

958-3 

1026-7 

1095-2 

1163-6 

1232-1 

41 

723-1 

795-4 

867-7 

940-0 

1012-3 

1084-6 

1  156-9 

1229-2 

1301-5 

4:| 

762-6 

838-9 

915-2 

991-4 

1067-7 

!  1144-0 

1220-2 

1296-5 

1372-8 

4j 

803-3 

883-7 

964-0 

1044-3 

1124-7 

1205-0 

1285-3 

1365-7 

1446-0 

5 

844-8 

929-3 

1013-8 

1098-2 

1182-7 

1267-2 

1351-7 

1436-2 

1520-6 

5k 

887-8 

976-6  1065-4 

1154-2 

1243-0 

!  1331-8 

1420-5 

1509-3 

1598-1 

54 

931-7 

1024-8 

1118-0 

1211-2 

1304-4 

1397-5 

1490-7 

1583-9 

1677-0 

51 

976-6 

1074-2 

1171-9 

1269-5  1367-2 

1464-9 

1562-5 

1660-2 

1757-8 

5£ 

1022-4  1124-6 

1226-9 

1329-1 

1431-4 

1533-6 

1635-8 

1738-1 

1840-3 

5| 

J  069-5  '1176-5 

1283-4 

1390-4 

1497-3 

1604-3 

1711-2 

1818-2 

1925-2 

52 

1117-6 

1229-3  1341-1 

1452-8  1564-6 

1676-3 

1788-1 

1899-9 

2011-6 

5£ 

1160-0 

1283-4 

1400-1 

1516-7 

1633-4 

1750-1 

1866-7 

1983-4 

2100-1 

6 

12296 

1338-3 

1460-0 

1581-6 

1703-3 

1825-0 

1946-6 

2068-3 

2190-0 

(J4 

1320-4 

1452-4 

1584-4  i  1716-5 

1848-6 

1980-6 

2112-6 

2244-7 

237b-7 

(>d 

1428-2 

1571-0 

1713-8 

1856-6 

1999-4  2142-2 

2285-1 

2427-9 

2570-7 

6| 

1540-1 

1694-1 

1848-1 

2002-2 

2056-2 

2310-2 

2464-2 

2618-2 

2772-2 

7 

1656-3 

1822-0 

1987-6 

2153-2 

2318-8 

2484-5 

2650^1 

2815-7 

2981-4 

74 

1776-7!  1954-4 

2132  1 

2309-7 

2487-4;  2665-1 

2842-8 

3020-4  3198-1 

?<| 

1901-4  2091-5 

2281-6 

2471-8 

2661-9  2852-0 

3042-2 

W32-3  3422-4 

71 

2030-2 

2233-3 

2436-3 

2839-3  2842-3 

3045-4 

3248-4 

3451-4 

3u54-4 

8 

2163-4 

2379-7 

2596-0 

2812-4 

3028-7 

3245-0 

3461-4 

3677-7 

3894-0 

£4 

2300-7 

2530-7 

2760-8  2990-9  3220-9  3451-0 

36*1-1 

3911-1  4141-2 

8£ 

2442-2 

2686-4 

2930-6  3174-9,3419-1 

3663-3  3907-5 

4151-7 

4396-0 

8| 

2588-0 

2846-8 

3105-6 

3364-4:3623-2 

3882-0 

4140-8 

4399-6 

4658-4 

, 

2737-9 

3011-7 

3285-5  1  3559-3 

3833-1 

4106-9 

4380-7 

4654-5 

4928-3 

114  PRACTICAL    TABLES 

TABLE    I  —  SaUARE    IRON 


size. 

1ft. 

2ft. 

3ft. 

4ft. 

5ft. 

6ft. 

7ft 

8ft. 

9ft. 

inch. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

94 

289-2 

578-4 

867-7 

1156-9 

1446-1 

1735-3 

2024-5 

2313-8 

2603-0 

305-1 

610-1 

915-2 

1220-2;  1525-3 

1830-3 

2135-4 

2440-4 

2745-5 

9! 

321-3 

642-7 

964-0 

1285-3 

1606-7 

1928-0 

2249-3 

2570-7 

2892-3 

10 

337-9 

675-8 

1013-8 

1351-7 

1689-6 

2027-5 

2365-4 

2703-4 

3041-0 

104 

355-1 

710-3 

1065-4 

1420-5 

1775-7 

2130-8 

2486-0 

2841-1 

3196-2 

372-7 

745-3 

1118-0  1490-7 

1863-4 

2236-0 

2608-7 

2981-4 

3354-0 

10| 

390-6 

781-3 

1171-9 

1562-5 

1953-1 

2343-8 

2734-4 

3125-0 

3515-7 

11 

409-0 

817-9 

1226-9 

1635-8 

2044-8 

2453-8 

2862-7 

3271-7 

3680-6 

114 

427-8 

855-6 

1283-4 

1711-2  2139-1 

2566-9 

2994-7 

3422-5 

3850-3 

Hi 

447-0 

894-0 

1341-1 

1788-1  2235-1 

2682-1 

3129-2 

3576-2 

4023-2 

HI 

466-7 

933-4 

1400-1 

1866-7 

2333-4 

2800-1 

3266-8 

3733-5 

4200-2 

J2 

486-7 

973-3 

1460-0 

1946-6 

2433-3 

2919-9 

3406-6 

3893-2 

437»-t 

PRACTICAL    TABLES.  115 

TABLE    1.  — SQUARE    IRON. 


size. 

10  ft. 

lift. 

12ft. 

13ft. 

14ft. 

15ft. 

16ft. 

17ft. 

18ft 

inch. 

Ibs. 

Ibs. 

ll.s. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ihs. 

Ibs. 

94 

2892-2  '3181  -4  !  3470-6  3759-9 

4049-1 

4338-3  j  4627-5  4916-7  5206-0 

94 

31)50-6  3355-6  3660-7 

3965-7 

4270-8 

4575-8  !  4880-9  5186-0  5491-0 

9$ 

3213-3 

3534-7 

3856-4 

4177-3 

44U8-6 

4020-0 

5141-3 

5462-6 

5784-0 

10 

3379-2 

3717-1 

4055-0 

4393-0 

4730-9 

5068-8 

5406-7 

5744-6 

6082-6 

104 

3551-4  3906-5  4261-6 

4616-8 

4971  -9  1  5327-0  5682-2  6037-3  6392-4 

104 

3726-7  4099-4  4472-1 

4844-7 

52  17-4  1  5590-1  5962-8  r  6335-4 

6708-1 

101 

3906-3 

4297-0 

4687-5 

5078-2 

5468-8 

5859-4 

6250-0 

6644-7 

7031-3 

11 

4089-6 

4498-6 

4907-5 

5316-5 

5725-4 

6134-4 

6543-4 

6952-3 

7361-3 

Ml 

4278-1  47  5-9  5133-7  5561-6 

5989-4 

6417-2 

6845-0;  7272-8 

7700-6 

114 

4470-2  4917-3  5364-3  581  1-3  6258-3 

6705-4 

7  152-4;  7599-4 

8046-4 

111 

4666-8  5133-5  5600-2  6066-9  6533-6 

7000-3 

7466-9  7933-6 

8400-3 

! 

12 

4S66-6 

5353-2  5839-9 

6326-5 

6?.13~2 

7299-8 

7786-5 

8273-2 

8759-8 

116  PRACTICAL    TABLES. 

TABLE    II  —  ROUND    I3LON. 


size. 

1ft 

2ft 

3ft. 

4ft 

5ft, 

6ft. 

7ft 

8ft 

9ft 

inch. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ib3. 

k 

0-2 

0-3 

0-5 

0-7 

0-8 

1-0 

1*2 

1*3 

1.5 

1 

0-4 

0-7 

1-1 

1-5 

1*9 

2-2 

2-6 

30 

3*4 

i 

0-7 

1-3 

2*0 

2-7 

3*3 

4-0 

4-6 

5-3 

6-0 

i 

1-0 

2-1 

3-1 

4-2 

5-2 

6*3 

7*3 

8-3 

9-4 

I 

1*5 

3-0 

4-5 

6*0 

7-5 

9-0 

10*5 

11*9 

13-4 

1 

2*0 

4-1 

.  6-1 

8-1 

10*2 

12-2 

14*2 

16-3 

18-3 

i 

2*7 

5-3 

8-0 

10-6 

13*3 

15*9 

18*6 

21*2 

23*9 

U 

3-4 

6-7 

10-1 

13-4 

16-8 

20-2 

23-5 

26-9 

30-2 

H 

4-2 

8-3 

12*5 

16-7 

20*9 

25*0 

29*2 

33-4 

37-5 

11 

5-0 

10-0 

15-1 

20*1 

25-1 

30-1 

35-1 

40*2 

45-2 

U 

6-0 

11-9 

17-9 

23-9 

29-9 

35-8 

41-8 

47-8 

53-7 

11 

7-0 

14-0 

21-0 

28*0 

35-1 

42*1 

49-1 

56*1 

63-1 

1| 

8*1 

16-3 

24-4 

32-5 

40-6 

48*8 

56-9 

65-0 

732 

« 

9*3 

18-7 

28-0 

37*3 

46-7 

56*0 

65*3 

74*7 

84-0 

2 

10-6 

21-2 

31-8 

42*5 

53*1 

63-7 

74-3 

84-9 

95*5 

2J 

12-0 

24-0 

36-0 

480 

59*9 

71*9 

83-9 

95-9 

107*9 

2| 

13-5 

26-9 

40-3 

53-8 

67-2 

80*6 

94-1 

107-5 

121*0 

2f 

15-0 

30*0 

44-9 

60-0 

74-9 

89-9 

104-8 

119-8 

134-8 

16-7 

33-4 

50-1 

66-8 

83*4 

100*1 

116-8 

133-5 

150-2 

21 

18-8 

36-6 

54-9 

73-2 

91-5 

109*8 

128*1 

146-3 

164-6 

21 

20*1 

40-2 

60-2 

80-3 

100-4 

120-5 

140-5 

160*6 

180*7 

2£ 

21*9 

43-9 

65*8 

87*8 

109-7 

131-7 

153-6 

175-6 

197-5 

3 

23*9 

47-8 

717 

95-6 

119-4 

143-3 

167-2 

1911 

215-0 

3& 

25-9 

51*9 

77-8 

103-7 

129-6 

155*6 

181-5 

207-4 

233-3 

3i 

28-0 

56-1 

84-1 

112-2 

140*2 

168*2 

196-3 

224*3 

253-4 

3| 

30-2 

60-5 

90*7 

121-0 

151-2 

181-4 

211-7 

241-S 

272-2 

3£ 

32-5 

65-0 

97-5 

l'0-O 

162*6 

195-1 

227-6 

260-1 

292-6 

3| 

34-9 

69-8 

104-7 

139-5 

174*4 

209-3 

244-2 

279*1 

314*0 

31 

37-3 

74-7 

l.'9-O 

149*3 

186-7 

224-0 

261-3 

298-7 

336*0 

3& 

39-9 

79*7 

•*  >j 

159-5 

199*3 

239*2 

279*0 

318*9 

358*8 

1 

1 

PRACTICAL    TABLES. 
TABLE    II.  —  ROTTND    IRON. 


11? 


size. 

10ft 

lift. 

12ft. 

13ft. 

14  ft 

15ft. 

16ft. 

17ft. 

18ft 

inch. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

i 

1-7 

1-8 

2-0 

2-1 

2-3 

2-5 

2-6 

2*8 

3-0 

§ 

3-7 

4-] 

4-5 

4-8 

5-2 

5-6 

6-0 

6-3 

6-7 

h 

6-6 

7-3 

8-0 

8-6 

9-3 

9-9 

10-6 

11-3 

11-9 

1 

10-4 

11-5 

12-5 

13-6 

14-6 

15-6 

16-7 

i7-3 

18-8 

1 

14-9 

16-4 

17-9 

19-4 

20-9 

22-4 

23-9 

25-4 

26-9 

i 

20-3 

22-4 

24-4 

26-4 

28-4 

30-5 

32-5 

34-5 

36-6 

1 

26-5 

29-2 

31-8 

34-5 

37-2 

39-8 

42-5 

45-1 

47-8 

U 

33-6 

37-0 

40-3 

43-7 

47-0 

50-4 

53-8 

57-1 

60-5 

1* 

41-7 

45-9 

50-1 

54-2 

58-4 

62-6 

66-8 

70-9 

75-1 

U 

50-2 

55-2 

60-2 

65-2 

70-3 

75-3 

80-3 

85-3 

90-3 

U 

59-7 

65-7 

71-7 

77-6 

83-6 

89-6 

95-6 

101-5 

107-5 

If 

70-1 

77-1 

84-1 

91-1 

98-1 

105-2 

112-2 

119-2 

126-2 

11 

81-3 

89-4 

97-5 

105-7 

113-8 

121-9 

130-0 

138-2 

146-3 

H 

93-3 

102-7 

112-0 

121-3 

130-7 

140-0 

149-3 

158-7 

168-0 

2 

106-9 

116-8 

127-4 

138-0 

148-6 

159-2 

169-9 

180-5 

192-1  1 

2£ 

119-9 

131-9 

143-9 

155-8 

167-8 

179-8 

181-8 

193-8 

205-8 

2i 

134-4 

147-8 

161-3 

174-7 

188-2 

201-6 

215-0 

228-5 

241-9 

2§ 

149-8 

164-7 

179-7 

194-7 

209-7 

224-6 

239-6 

254-6 

269-6 

2i 

166-9 

183-6 

200-3 

216-9 

233-6 

250-3 

267-0 

283-7 

300-4 

2| 

182-9 

201-2 

219-5 

237-8 

256-1 

274-4 

292-7 

311-0 

329-3 

21 

iOO-8 

220-8 

240-9 

261-2 

281-1 

301-1 

321-2 

341-3 

361-4 

2£ 

219-4 

241-4 

263-4 

285-3 

307-2 

329-2 

351-1 

373-0 

395-0 

5 

JJ38-9 

262-8 

286-7 

310-5 

334-4 

358-3 

382-2 

406-1 

430-0 

31 

259-3 

285-2 

311-1 

337-0 

363-0 

388-9 

414-8 

440-7 

466-7 

3* 

280-4 

308-4 

336-5 

364-5 

392-6 

420-6 

448-6 

476-7 

504-7 

3! 

302-4 

332-6 

362-9 

393-1 

423-4 

453-6 

483-8 

514-1 

544-3 

3i 

325-1 

357-6 

390-1 

422-7 

455-2 

487-7 

520-2 

552-7 

585-2 

3| 

3489 

383-7 

418-6 

453-5 

488-4 

523-3 

558-2 

593-1 

627-9 

31 

3733 

410-7 

448-0 

485-3 

522-6 

560-0 

597-3 

634-6 

672-0 

31 

3986 

438-5 

478-4 

518-2 

558-1 

598-0 

637-8 

677-7 

717-6 

^ 

118                             PRACTICAL    TABLES. 

TABLE    11  —  ROUND    IRON. 

size. 

1ft 

2ft. 

3ft. 

4ft. 

5ft. 

6ft. 

7ft. 

8ft 

9ft. 

inch. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

4 

42-5 

84-9 

127-4 

169-9 

21-2-3 

254-8 

297-2 

339-7 

382-2 

4j 

45-2 

,90-3 

135-5    180-7 

sSn-9 

27  K 

316-2 

3)1-4 

406-6 

4i 

48-0 

95-9 

143-9     191-8 

239-8 

287-7 

335-7    383-6 

431-6 

41 

50-8 

101-6 

152-4  1  203-3 

254-1 

304-9 

355-7     40i-5 

457-3 

44 

53-8 

107-5 

161-3 

215-0 

268-8 

322-0 

37fi-3    43.)-  1 

483-8 

4| 

56-8 

113-6 

170-4 

227-2 

283-9 

34U-7 

397-5    454-3 

511- 

41 

60-0 

1  19-8 

179-7 

239-t 

299-5 

359-4 

419-3;   479-2 

539- 

4$ 

63-1 

126-2 

189-3 

252-4 

315-5 

378-6 

441-7 

504-8 

567-8 

5 

66-8 

133-5 

200-3 

267-0 

333-8 

400-5 

467-3 

534-0 

600-8 

5$ 

69-7 

139-5 

209-2    278-9 

348-7 

418-4 

488-1 

557-8 

627-6 

5i 

7*2 

146-3 

2  1  9-5  j   292-7 

3(55-9 

439-0 

51-2-2 

585-4 

658-5 

5* 

76-7 

153-4 

23<HJ  315-8 

383-5 

4o()"2 

53f>-9 

613-6 

6903 

54 

80-3 

160-6 

24'HJ    321-2 

401-5 

481-8 

562-1 

642-4 

722-7 

51 

84-0 

1(58-0 

252-0    336-0 

420-0 

504-0 

588-0 

1  572-1 

75<H 

5:| 

87-8 

175-6 

263-3    351-1 

438-9 

5-2;  i-7 

614-4 

702-2 

79:)-0 

i>J 

91-6 

183-3 

274-9 

366-5 

458-2 

549-8 

641-4 

733-1 

824-7 

tf 

95-6 

191-1 

286-7 

382-2 

477-8 

573-3 

668-9 

764-4 

860-0 

6| 

103-7 

207-4 

311-1 

414-8 

518-5 

622-2 

725-9 

829-6 

933-3 

64 

112-2 

224-3 

336-5 

448-6 

560-8 

673-0 

785-1 

897-3 

1009-4 

61 

121-0 

241-9 

362-9 

483-8 

604-8 

725-8 

846-7 

967-6 

1088-6 

7 

130-0 

260-1 

390-1 

520-2 

650-2 

780-3 

910-3 

1040^4 

1170-4 

74 

139-5 

279-1 

418-6 

558-2 

697-7 

837-3 

976-8 

1116-4 

1255-9 

74 

149-3 

298-7 

448-0 

597-3 

741-6 

896-0 

1045-3  1  1194-6 

1344-0 

71 

159-5 

318-9 

478-4 

637-8 

797-3 

956-7 

1116-2 

1275-6 

1435-1 

8 

169-9 

339-7 

509-6 

679-4 

849-3 

1019-1 

1189-0 

1358-8 

1528-7 

at 

180-7 

361-4 

542-1 

722-8 

903-5 

1084-2 

1264-9 

1445-6 

1626-3 

84 

191-8 

383-6 

595-4 

767-2 

959-0 

1150-8 

1342-6 

1534-5 

172(5-3 

81 

203-3 

406-5 

609-8 

813-0 

1016-3 

1219-6 

422-8 

1626-1 

1829-3 

9 

215-0 

430-1 

645-1 

860-2 

1075-2 

1290-2 

505-3 

1720-3 

1935-4 

PRACTICAL    TABLES.  119 

TABLE    II.  — ROUND    IRON. 


r   - 
size 

10ft 

lift. 

12ft 

tan 

14ft. 

15ft.!l(jft 

17ft. 

18ft 

inch. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

4 

424-6 

467-1 

509-( 

552M 

594-5 

637-0    676-4     721-9 

7(i4-4 

4| 

451-7 

496-9 

54-2-1 

587-q 

632-4 

677-6    722-8    761-0 

313-1 

44 

479-5 

527-5 

575-4 

623-4 

671-3 

719-3    767-2    815-2 

603-1 

4| 

508-2 

559-0 

609-8 

660-  6  i   711-4 

762-2    813-0    8(53-9 

914-7 

4i 

537-b 

591-4 

645-1 

698-9 

752-6 

806-4    860-2    913-9 

9J!7-7 

41 

567-9 

624-7 

681-5 

738-2 

795-0 

851-8    908-r 

9;>5-4 

1022-2 

41 

599-0 

658-9 

718-8 

778-7 

838-6 

898-5    958-4  1018-3 

1078-2 

4i 

630-9 

694-0 

757-1 

820-2 

883-3 

946-4  1009-5 

!  1072-6 

1135-7 

5 

667-5 

734-3 

801-0 

867-8 

934-5 

1001-3 

'  1068-0 

1  134-8 

1201-5 

5£ 

697-3 

767-0 

830-8 

906-5 

976-2 

1046-0  HI5-7JliaV4 

1255-2 

54 

731-7 

804-9 

878-1 

951-2 

1024-4 

K)97-() 

1  1  70-8  i  1243-9 

1317-1 

767-0 

813-7 

920-4 

997-1 

1073-8  1150-5 

1227-2 

1383-9 

1380-6 

5d 

803-0 

883-3 

9fi3-6 

1044-1 

1124-3 

1204-6 

1284-9 

1365-2 

1445-5 

5| 

840-0 

924-0 

1008-0 

1092-0 

1176-0 

1260-0 

1344-0 

1428-0 

1512-0 

51 

877-8 

965-5 

1053-3 

1141- 

1228-9  j  131  6-6 

1404-4 

1492-2 

1580-0 

5| 

916-3 

1008-0 

1099-6 

1191-2 

1282-9 

1374-5 

1466-1 

1557-8 

1649-4 

6 

955-5 

1051-1 

1146-6 

1242-2 

1337-7 

1433-3 

1528-8 

1624-4 

1719-9 

04 

1037-0 

1140-7 

1244-4 

1348-2 

1451-9 

1555-6 

1659-3 

1763-0 

1866-7 

0* 

1121-6 

1233-8 

1345-9 

1458-1 

1570-2 

1682-4 

1794-6 

1906-7 

'2018-9 

01 

1209-6 

1330-6 

1451-5 

1572-5 

1693-4 

1814-4 

1935-4 

2056-3 

2177-3 

7 

1300-5 

1430-5 

1560-6 

1690-6 

1820-7 

1950-7 

2088-8 

2210-8 

2340-9 

74 

1395-4 

1535-0 

1674-5 

1814-1 

1953-6 

2093-2  2232-7 

2372-2  2511-8 

74 

1493-3 

1642-6 

1791-9 

1941-3 

2090-6 

2339-9 

2389-2 

2538-6  2687-9 

71 

1594-6 

1754-0 

1913-5 

2072-9 

2232-4 

2391-8 

2551-3 

2710-8  2870-2 

8 

1698-6 

1868-4 

2038-3 

2208-1 

2378-0 

£547-8 

2717-7 

2887-6 

3057-4 

84 

18  f9-0 

1987-7 

2168-4 

2349-0 

2529-7 

2740-4 

2891-1 

3071-813252-5 

84 

1918-1 

2109-9 

2301-7 

2493-5 

2685-3 

2879-1 

30(58-9 

3260-7  !  3452-5 

81 

2032-6 

2235-9 

2439-1 

2642-4 

2845-6 

3048-9 

3252-2 

3455-4 

3658-7 

9 

2150-4 

2365-4 

2580-5 

2795-5 

30106 

3225-6 

3440-6 

3655-7  , 

J870-7 

11 


1 

\ 

J20                            PRACTICAL    TABLES. 

TABLE   II.  —  ROUND    IRON. 

size. 

1ft. 

2ft. 

3ft.    4ft. 

5ft. 

6ft. 

7ft. 

8ft. 

9ft. 

inch. 

Ibs. 

Ibs. 

Ibs.       Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Q| 

227-2 

454-3 

681-5    908-6 

1135-8 

1362-9 

1590-1 

1817-2 

2044-4 

CU 

239-6 

479-2 

718-8    958-4 

1198-0 

1437-6 

1677-2 

1916-8 

2156-4 

!    9| 

252-4 

505-8 

757-1  1009-5 

1261-9 

1514-3 

1766-6 

2019-0 

2291-4 

10 

266-3 

532-6 

798-9  1065-2 

1331-4 

1597-7 

1864-0 

2130-3 

2396-6 

lOi 

278-9 

557-8 

836-8  lllf»-7 

1394-6 

1673-5 

1952-5 

2231-4  2510-3 

10£ 

292-7 

585-4 

878-1  1170-8 

1463-4 

1756-1 

2048-8  2341-5  2(534-2 

101 

306-8 

603-6 

920-4  1227-2 

1534-0 

1840-8 

2147-6 

2454-4 

2761-2 

11 

321-2 

642-4 

963-6  1284-9 

1606-1 

1927-3 

2248-5 

2569-7 

2890-9 

Hi 

336-0 

672-0 

1008-0  1344-0 

1680-0 

2016-0 

2352-0 

2688-0 

3024-0 

in 

351-1 

702-2 

1053-3  1404-4 

1755-5 

2106-6  2457-7 

2808-8 

3159-9 

in 

366-5 

733-1 

1099-6  14-36-1 

1832-7 

2199-2 

'2565-8 

2932-3 

3298-8 

12 

382-2 

764-4 

1146-6  1528-8 

1911-0 

2293-2 

2675-5 

3057-7 

3439-9 

... 

PRACTICAL   TABLES.  121 

TABLE    II.  —  ROUND    IRON. 


size. 

10  ft. 

lift. 

12ft. 

13ft. 

14ft. 

15ft. 

16ft. 

17ft. 

18ft. 

inch. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

9i 

2271-5 
2396-0 

2498-7 
2635-6 

2725-8 
2875-2 

2953-0 
3114-8 

3180-1 
3354-4 

3407-3 
3594-0 

3634-4 
3833-6 

3861-6 
4073-2 

4088-7 
4312-8 

91 

2523-8 

2776-1 

3028-5 

3280-9 

3533-3 

3785-6 

4038-0 

4290-4 

4542-8 

10 

2662-9 

2929-2 

3195-5 

3461-7 

3728-0 

3994-3 

4260-6 

4526-9 

4793-2 

10| 

2789-2 

3068-2 

3347-1 

3626-0 

3904-9 

4183-9 

4462-8 

4741-7 

5020-6 

10£ 

2926-9 

3219-6 

3512-3 

3804-9 

4097-6 

4390-3 

4683-0 

4975-7 

5268-4 

101 

3068-0 

3374-8 

3681-6 

3988-4 

4295-2 

4602-0 

4908-8 

5215-6 

5522-4 

11 

3212-2 

3533-4 

3854-6 

4175-8 

4497-0 

4818-2 

5139-5 

5460-7 

5781-9 

m 
iu 

3360-0 
3511-0 

3696-0 
3862-1 

4032-0 
4213-2 

4368-1 
4564-4 

4704-1 
4915-5 

5040-1 
5266-6 

5376-1 
5619-7 

5712-1 

5968-8 

6048-1 
6319-9 

111 

3665-4 

4031-9 

4398-4 

4765-0 

5131-5 

5498-0 

5864-6 

6231-1 

6597-6 

12 

3822-1 

4204-3 

4586-5 

4968-7 

5350-9 

5733-1 

6115-3 

6497-5 

6879-7 

22                             PRACTICAL    TABLES. 

TABLE    III.  —  FLAT   IRON. 

• 

Th'k. 

Wid.   1  ft 

2ft 

:jftj 

4ft 

511 

<>ft 

7ft 

8ft|9ft 

inzh. 

ir.ch. 

Ihs. 

Ihs. 

ll.s. 

n.s. 

Ibs. 

U.s. 

Ihs. 

lt>3. 

Ibs. 

4 

1 

0-8 

1-7 

2-5 

3-4 

4-2 

5-1 

5-9 

6-8      76 

4 

14 

1-1 

2-1 

3-2 

4-2 

5-3 

6-3 

7-4 

8-4 

9-5 

4 

u 

1-3 

2-5 

3-8 

5-1 

6-3 

7-6 

8-9 

KM 

114 

~ 

4 

u 

1*5 

3-0 

4-4 

5-9 

7-4 

8-9 

10-4 

11*6 

13-3 

i 

2 

1-7 

3-4 

Sri 

6-8 

8-5 

10-1 

11  '8 

13-5 

15-2 

4 

24 

1-9 

3-8 

5-7 

7-6 

9-5 

11-4 

13-3 

15-2 

17-1 

4 

2d 

2-1 

4-2 

H-3 

8-4 

10-fi 

12-7 

14-8 

16'9 

190 

4 

25 

2-3 

4-ti 

7-0 

9-3 

11-6 

13-9 

16-3 

18-6 

209 

4 

3 

2-5 

5-1 

7-fi 

1  0-1 

12-7 

15-2 

17-7 

20-3 

228 

4 

si 

2-7 

5-.r> 

8-2 

II  -ii 

13-7 

16-5 

19-2 

2-2-0 

24-7 

4 

34 

3-0 

5-9 

8-9 

ll-H 

14-8 

17-7 

20-7 

23-7 

2G-G 

4 

31 

3-2 

6-3 

9-5 

12-7 

15-8 

19-0 

32-J 

25-4 

28-5 

4 

4 

3-4 

6-8 

in-i 

13-5 

KV9 

20-3 

23-7 

27-0 

30-4 

4 

44 

3-H 

7-2 

1  08 

14-4 

18-0 

21-5 

25-1 

28-7 

32-3 

4 

4i 

3-8 

7-<i 

11-4 

1.V2 

19-0 

22-8 

26-6 

30-4 

34-2 

4 

42 

4-0 

8-0 

12-0 

16-1 

20-1 

24-1 

28-1 

32-1 

36-1 

4 

5 

4-2 

8-4 

12-7 

lfi-9 

21-1 

25-3 

29-6 

33-8 

38-0 

4 

54 

4.4 

8-9 

13-3 

17-7 

22-2 

26-6 

31-1 

3.rf> 

39-9 

4 

M 

4-6 

9-3 

13-9 

18-6 

23-2 

27-9 

3r>-5 

37-2 

41-8 

4 

51 

4-9 

9-7 

146 

19-4 

24-3 

29-2 

34-0 

38-9 

43-7 

4 

G 

5-1 

10-1 

15-2 

20-3 

25-3 

30-4 

35-5 

40-6 

45-6 

1 

1 

1-3 

2-5 

3-8 

5-1 

6-3 

7-6 

8-9 

10-1 

11-4 

8 

1-6 

3-2 

4-8 

6-3 

7-9 

9-5 

11-1 

12-7 

14-3 

li 

1-9 

3-8 

5-7 

7-b 

9-5 

IM 

13-3 

15-2 

17-1 

1 

U 

2-2 

4.4 

6-7 

8-9 

11-1 

*«3-3 

15-5 

17-7 

20-0 

| 

2 

2-5 

5-1 

7-6 

10-1 

12-7 

15-2 

17-7 

20-3 

22-8 

ft 

2* 

2-9 

5-7 

8-3 

11-4 

14-3 

17-1 

20-0 

22-8 

25-7 

| 

2-i 

3-2 

6-3 

9-5 

12-7 

15.-8 

19-0 

22-2 

25-4 

28-5 

PRACTICAL    TABLES. 


123 


TABLE    III.  — FLAT    IRON. 


Th'k. 

Wid.  10ft'  lift 

12ft 

13ft 

14ft 

15ft 

16ft 

17ft 

18ft 

inch. 

inch. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

^ 

1 

8-5 

9-3 

10-1 

Jl-0 

11-8 

12-7 

13-5 

14-4 

15-2 

4 

H 

10-6 

11-6 

12-7 

13-7 

14-8 

15-8 

16-9 

17-9 

19-0 

k 

U 

12-7 

13-9 

15-2 

1G-5 

17-7 

19-0 

20-3 

21-5 

22-8 

i 

11 

14-8 

16-3 

17-7 

19-2 

20-7 

22-2 

23-7 

25-1 

26-6 

j 

2 

16-9 

18-6 

20-3 

22-0 

23-7 

25-4 

27-0 

28-7 

30-4 

^ 

2i 

19-0 

20-9 

22-8 

24-7 

2G-6 

28-5 

30-4 

32-3 

34-2 

^ 

2£ 

21-1 

23-2 

25-3 

27-5 

29-6 

31-7 

33-8 

35-9 

38-0 

1 

21 

23-2 

25-6 

27-9 

30-2 

32-5 

34-9 

37-2 

39-5 

41-8 

£ 

3 

26-3 

27*9 

30-4 

33-0 

35-5 

38-0 

40-6 

43-1 

45-6 

£ 

3* 

27-5 

30-2 

33-0 

35-7 

38-5 

41-3 

43-9 

46-7 

49-4 

| 

a* 

29-6 

32-5 

35-5 

38-5 

41-4 

44.4 

47-3 

50-3 

53-2 

i 

31 

31-7 

34-9 

38-0 

41-2 

44-4 

47-5 

507 

53-9 

57-0 

^ 

4 

33-8 

37-2 

40-6 

43-9 

47-3 

50-7 

54-1 

57-5 

60-8 

£ 

4| 

35-9 

39-5 

43-1 

46-7 

50-3 

53-9 

57-5 

61-0 

64-6 

\ 

;>8-o 

41-8 

45-6 

49-4 

53-2 

57-0 

60-8 

64-6 

68-4 

k 

4| 

40-1 

44-1 

48-2 

52-2 

56-2 

60-2 

64-2 

68-2 

72-2 

| 

5 

42-2 

46-5 

50-7 

54-9 

59-1 

63-4 

65-6 

71-8 

76-0 

i 

44-4 

48-8 

53-2 

57-7 

62-1 

66-5 

71-0 

75-4 

79-9 

54 

46-5 

51-1 

55-8 

60-4 

65-1 

69-7 

74-4 

79-0 

83-6 

i 

51 

48-6 

53-4 

58-3 

63-2 

68-0 

72-9 

77-7 

82-6 

87-5 

i 

6 

50-7 

55-8 

60-8 

65-9 

70-9 

76-0 

81-1 

86-2 

91-2 

| 

I 

12-7 

13-9 

15-2 

16-5 

17-7 

19-0 

20-3 

21-5 

22-8 

i 

11 

15-8 

17-4 

19-0 

20-6 

22-2 

23-8 

25-3 

28-9 

28-5 

8 
3 

••-4 

19-0 

20-9 

22-8 

24-7 

26-6 

28-5 

30-4 

32-3 

34-2 

8 
1 

« 

22-2 

24-4 

26-6 

28-8 

31-1 

33-3 

35-5 

37-7 

39-9 

. 

2 

25-3 

27-9 

30-4 

33-0 

35-5 

38-0 

40-6 

43-1 

45-6 

i 

28-5 

31-4 

34-2 

37-1 

39-9 

42-8 

45-6 

48-5 

51-3 

8 
1 

2i 

31-7 

34-9 

38-0 

41-2 

44.4 

47-5 

50-7 

53-9 

57-0 

ft 

i 

124 

PRACTICAL    TABLES, 

TABLE    ill.  —  FLAT    IRON. 

Th'k.  Wid.  1ft 

2ft!  3ft  4ft   5ft  6it  7ft   8ft 

9ft 

inch.      inrh.     Ibs.  . 

Ibs.     Ibs. 

Ibs. 

Ibs.  i  Ibs.     Ibs.  |  Ibs. 

Ibs. 

1 

21 

3-5 

7-0 

10-5 

13-9 

17-4 

20-9 

24-4 

27-9 

31-4 

1 

3 

3-8 

7-6 

11-4 

152 

19-0 

22-8 

26-6 

30-4 

34-2 

1 

34 

4-1 

8-2    12-4 

16-5 

20-6 

24-7 

28-8 

33-0 

37-1 

f 

3d 

4.4 

8-9 

13-3 

17-7 

22-2 

26-6 

31-1 

35-5 

39-9 

f 

31 

4-8 

9-5 

14-3 

19-0 

23-8 

28-5 

33-3 

38-0 

42-8 

§ 

4 

5-1 

10-1 

15-2 

20-3 

25-3 

30-4 

35-5 

40-6 

45-6 

1 

44 

5-4 

10-8 

16-1 

21-5 

26-9    32-3 

37-7 

43-1 

48-5 

§ 

4i 

5-7 

11-4 

17-1 

22-8 

28-5 

34-2 

39-9 

45-6 

51-3 

f 

41 

6-0 

12-0 

18-1 

24-1 

30-1 

30-  1 

42-1 

48-2 

54-2 

§ 

5 

f>-3 

12-7 

19-0 

25-3 

31-7 

38-0 

44-4 

50-7 

57-0 

1 

54 

G-7 

13-31  20-0 

1 

26-fi 

33-3 

39-9 

46-fi 

53-2 

59-9 

f 

5«£ 

7-0 

13-9 

20-9 

27-9 

34-9 

41-8 

48-8 

55-8 

62-7 

f 

51 

7-3 

14-6 

2J-9 

29-2 

36-4 

43-7 

51-0 

58-3 

65-6 

§ 

6 

7-6 

15-2 

22-8 

30-4 

38-0 

45-6 

53-2 

60-8 

68-4 

i 

1 

1-7 

3-4 

5-1 

6-8 

8-5 

10-1 

11-8 

13-5 

15-2 

i 

M 

2-1 

4-2 

6-3 

8-4 

10-6 

12-7 

14-8 

1G-9 

190 

£ 

1} 

2-5 

5-1 

7-6 

10-1 

12-7 

15-2 

17-7 

20-3 

22-8 

h 

11 

3-0 

5-9 

8-9 

1J-8 

14-8 

17-7 

20-7 

23-7 

2G-6 

| 

2 

3-4 

6-8 

10-1 

13-5 

16-9 

20-3 

23-7 

27-0 

30-4 

g 

2| 

3-8 

76 

11-4 

15-2 

19-0    22-8 

26-6 

30-4 

34-2 

} 

2d 

4-2 

8-4 

12-7 

109 

21-1  1  25-3 

29-6 

33-8 

3S-0 

4 

21 

4-6 

9-3 

13-9 

18-6 

23-2 

27-9 

32-5 

37-2 

4i-8 

4 

3 

5-1 

10-1 

15-2 

20-3 

25-3 

30-4 

35-5 

40-6 

45-6 

34 

5-5 

11-0 

16-5 

22-0 

27-5    32-9    38-4 

43-9 

49-4 

4 

34 

5-9 

11-8 

17-7 

23-7 

29-6;  35-5 

41-4 

47-3 

53-2 

4 

31 

6-3 

12-7 

19-0 

25-3 

31-7 

38-0 

44-4 

50-7 

57-0 

4 

4 

6-8 

13-5 

20-3 

27-0 

33-8 

40-6 

47-3 

54-1 

60-8 

PRACTICAL    TABLES.  125 

TABLE    III.  — FLAT    IRON. 


Th'k. 

Wid.  10ft  lift 

12ft 

13ft  14ft 

15ft 

16ft 

17ft 

18ft 

inch 

inch.     Ibs. 

Ihs. 

Ihs. 

Ihs. 

Ib*. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

1 

2| 

34-9 

36-3 

41-8 

45-3 

48-8 

52-3 

55-8 

59-3 

62-7 

§ 

3 

38-0 

41-8 

45-6 

49-4 

53-2 

57-0 

60-8 

64-6 

68-4 

3| 

41-2 

45-3 

49-4 

53-6 

57-7 

61-8 

65-9 

70-0 

74-2 

| 

44-4 

48-8 

53-2 

57-7 

62-1 

66-5 

71-0 

75-4 

79-9 

1 

32 

47-5 

52-3 

57-0 

61-8 

66-5 

71-3 

76-0 

80-8 

85-5 

| 

4 

50-7 

55-8 

60-8 

65-9 

70-9 

76-0 

81-1 

86-2 

91-2 

1 

44 

53-9 

59-3 

64-7 

70-0 

75-4 

80-8 

86-2. 

91-6 

97-0 

1 

44 

57-0 

62-7 

68-4 

74-2 

79-9 

85-6 

91-3 

97-0 

102-7 

1 

42 

60-2 

66-2 

72-2 

78-3 

84-3 

90-3 

96-3 

102-3 

108-4 

I 

5 

63-3 

69-7 

76-0 

82-4 

88-7 

95-0 

101-4 

107-7 

114-0 

i 

*M 

66-5 

73-2 

79-8 

86-5 

93-1 

99-8 

106-5 

113-1 

119-8 

1 

Si 

69-7 

76-7 

83-7 

90-6 

97-6 

104-5 

111-5 

118-5 

125-5 

1 

51 

72-9 

80-2 

87-5 

94-7 

102-0 

109-3 

116-6 

123-9 

131-2 

I 

6 

76-0 

83-6 

91-2 

98-9 

106-5 

114-1 

121-7 

129-3 

136-9 

£ 

1 

16-9 

18-6 

20-3 

22-0 

23-7 

25-4 

27-0 

28-7 

30-4 

£ 

H 

21-1 

23-2 

25-3 

27-5 

29-6 

31-7 

33-8 

35-9 

38-0 

i 

M 

25-3 

27-9 

30-4 

33-0 

35-5 

38-0 

40-6 

43-1 

45-6 

1 

H 

29-6 

3^-5 

35-5 

38-5 

41-4 

44-4 

47-3 

50-3 

53-2 

i 

2 

33-8 

37-2 

40-6 

43-9 

47-3 

50-7 

54-1 

57-5 

60-8 

i 

2| 

38-0 

41-8 

45-6 

49-4 

53-2 

57-0 

60-8 

64-6 

68-4 

I 

2£ 

42-2 

46-5 

50-7 

54-9 

59-1 

63-4 

65-6 

71-8 

76-0 

i 

21 

46-5 

51-1 

55-8 

60-4 

65-1 

69-7 

74-4 

79-0 

83-6 

£ 

3 

50-7 

55-8 

60-8 

65-9 

70-9 

76-0 

81-1 

86-2 

91-2 

i 

34 

54-9 

60-4 

65-9 

71-4 

76-9 

82-4 

87-9 

93-3 

98-8 

1 

3£ 

59-2 

65-1 

71-0 

76-9 

82-8 

88-7 

94-6 

100-6 

106-5 

i 

31 

63-3 

69-7 

76'0 

82-4 

88-7 

95-0 

101-4 

107-7 

114-0 

i 

4 

67-6 

74-4 

84-1 

87-9 

94-6 

101-4 

108-2 

114-9 

121-7 

1*26                              PRACTICAL    TABLES. 

'ABLE    III.  —  FLAT    IRON 

Th'k. 

Wd 

1ft 

2ft 

3ft 

ft  5 

5ft 

6ft 

J7« 

8ft 

9ft 

inch. 

inc'i. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

i 

41 

7-2 

14-4 

21-5 

•28-7 

35-9 

43-1 

50-3 

57-4 

64-6 

i 

4<i 

7-6 

15-2 

22-8 

30-4 

38-0 

45-6 

53-2 

60-8 

68-4 

i 

4| 

8-0 

16-1 

24-1 

32-1 

40-] 

48-2 

56-2 

64-2 

72-2 

i 

5 

8-4 

16-9 

25-3 

33-8 

42-2 

50-7 

59-1 

676 

76-0 

1 

5i 

8-9 

17-7 

26-6 

35-5 

44-4 

53-2 

62-1 

71-0 

79-9 

i 

5£ 

9-3 

18-6 

27-9 

37-2 

46-5 

55-8 

65-1 

74-4 

83-7 

i 

5| 

9-7 

19-4 

29-2 

38-9 

48-G 

58-3 

68-0 

77-7 

87-5 

h 

6 

10-1 

20-3 

30-4 

40-6 

50-7 

60.8 

70-9 

8M 

91-2 

I 

1 

2-1 

4-2 

6-3 

8-4 

10-6 

12-7 

14-8 

16-9 

19-0 

1 

« 

2-6 

5-3 

7-9 

10-6 

13-2 

15-8 

18-5 

21-1 

23-8 

I 

li 

3-2 

6-3 

9-5 

12-7 

15-8 

19-0 

22-2 

25-4 

28-5 

i 

11 

3-7 

7-4 

11-1 

14-8 

18-5 

22-2 

25-9 

29-6 

33-3 

1 

2 

4-2 

8-4 

12-7 

16-9 

21-1 

25-3 

29-9 

33-8 

38-0 

I 

2| 

4-8 

9-5 

14-3 

19-0 

23-8 

28-5 

33-3 

38-0 

42-8 

f 

24 

5-3 

10-6 

15-8 

21-1 

26-4 

31-7 

37-0 

42-2 

47-5 

1 

21 

5-8 

11-6 

17-4 

23-2 

29-0 

34-8 

40-7 

46-5 

52-3 

f 

3 

6-3 

12-7 

19-0 

25-3 

31-7 

38-0 

44.4 

50-7 

57-6 

t 

3* 

6-9 

13-7 

20-6 

27-5 

34-3 

41-2 

48-1 

54-9 

61-8 

f 

3J 

7-4 

14-8 

22-2 

29-6 

37-0 

44.4 

51-8 

59-2 

66-5 

f 

31 

7-9 

15-8 

23-8 

3J-7 

39-6 

47-5 

55-5 

63-4 

71-3 

f 

4 

8-4 

16-9 

25-3 

33-8 

42-2 

50-7 

59-1 

67-6 

76-0 

1 

4| 

9-0 

18-0 

26-9 

35-9 

44-9 

53-9 

62-9 

71-8 

80-8 

f 

4i 

9-5 

19-0 

28-5 

38-0 

47-5 

57-0 

66-5 

76-1 

85-6 

I 

41 

io-o 

20-1 

30-1 

40-1 

50-2 

60-2 

70-2 

80-3 

90-3 

i 

5 

.'.0-6 

21-1 

31-7 

42-3 

52-8 

63-4 

73-9 

84-5 

95-1 

f 

5i 

:.M 

22-2 

33-3 

44.4 

55-5 

66-5 

77-6 

88-7 

99-8 

f 

5i 

;l-6 

23-2 

34-9 

46-5 

58-1 

69-7 

81-3 

92-9 

104-6 

f 

5| 

12-1 

24-3 

38-4 

48-6 

60-7 

72-9 

85-0 

97-2 

109-3 

PRACTIC/L    TABLES.  127 

TABLE    III.— FLAT    IRON. 


Th'k. 

Wid. 

10ft 

lift 

12ft  13ft 

14ft 

15ft 

I6ft 

17ft 

18ft! 

inch. 

inch. 

Ihs. 

Ihs. 

;i>s. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

1 

41 

71-8 

7'J-O 

86-2 

93-4 

100-5 

107-7 

114-9 

122-1 

129-3 

i 

44 

76-0 

83-B 

91-2 

98-9 

106-5 

114-1 

121-7 

129-3 

136-9 

i 

41 

80-3 

88-3 

96-3 

104-3 

112-4 

120-4 

128-4 

136-4 

144-5 

i 

5 

84-5 

92-9 

101-4 

109-8 

118-3 

126-7 

135-2 

143-6 

152-1 

i 

51 

88-7 

97-6 

106-5 

115-4 

124-2 

133-1 

142-0 

150-8 

159-7 

i 

54 

93-0 

102-2 

111-5 

120-8 

130-1 

139-4 

148-7 

158-0 

167-3 

i 

5| 

97-2 

106-9 

116-6 

126-3 

136-0 

145.8 

155-5 

165-2 

174-9 

i 

6 

101-4 

111-5 

121-7 

131-8 

141-9 

152-1 

162-2 

172-4 

182-5 

l 

1 

21-1 

23-2 

25-3 

27-5 

29-6 

31-7 

33* 

35-9 

38-0 

i 

H 

26-4 

29-0 

31-7 

34-3 

37-0 

39-6 

42-2 

44-9 

47-5 

i 

14 

31-7 

34-8 

38-0 

41-2 

44.4 

47-5 

50-7 

53-9 

57-0 

t 

H 

37-0 

40-7 

44-4 

48-1 

51-8 

55-5 

59-2 

62-8 

66-5 

t 

2 

42-2 

46-5 

50-7 

549 

60-1 

63-4 

67-6 

71-8 

76-0 

I 

21 

47-5 

52-3 

57-0 

51-8 

66-5 

71-3 

76-0 

80-8 

85-5 

t 

24 

52-8 

58-1 

63-4 

68-6 

73-9 

79-2 

84-5 

89-8 

95-0 

t 

21 

58-1 

63-9 

69-7 

75-5 

81-3 

87-1 

92-9 

98-7 

104-5 

i 

3 

63-3 

69-7 

76-0 

82-4 

88-7 

95-0 

101-4 

107-7 

114-0 

i 

31 

68-7 

75-5 

82-4 

89-3 

96-1 

103-0 

109-9  116-7 

123-6 

t 

34 

73-9 

81-3 

88-7 

96-1 

103-5 

110-9 

118-3  125-7 

133-1 

i 

31 

79-2 

87-1 

95-1 

103-0 

110-9 

118-8 

126-8 

134-7 

142-6 

i 

4 

84-5 

92-9 

101-4 

109-8 

118-3 

126-7 

135-2 

143-6 

152-1 

i 

41 

89-8 

98-8 

107-8 

116-7 

125-7 

134-7 

143-7  152-6 

161-6 

i 

44 

95-1 

104-6 

114-1 

123-6 

133-1 

142-6 

152-1  161-6 

171-1 

$ 

41 

100-3 

110-4 

120-4 

130-4 

140-5 

150-5 

160-5  170-6 

180-6 

t 

5 

105-6 

116-2 

126-8 

137-3 

147-9 

158-4 

169-0  179-6 

190-1 

51 

110-9 

122-0 

133-1 

144-2 

155-3 

166-4 

177-5  188-5 

199-6 

i 

54 

116-2 

127-8 

139-4 

151-0 

162-6 

174-3 

185-9  197-5 

209-1 

i 

51 

121-5 

133-6 

145-7 

157-9 

170-0 

182-2 

194-3  206-5 

218-6 

128                             PRACTI^L    TABLES. 

TABLE    III  —  FLAT    IRON 

Thk. 

Wid. 

1ft 

2ft 

3ft 

4ft 

5ft  6ft 

7ft 

8ft 

9ft 

inch. 

inch. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs.     Ibs. 

Ibs. 

Ibs. 

Ibs. 

1 

6 

12-7 

25-3 

38-0 

50-7 

63-4 

76-0 

88-7 

101-4 

114-1 

1 

2-5 

5-1 

7-6 

10-1 

12-7 

15-2 

17-7 

20-3 

22-8 

3-2 

6-3 

9-5 

12-7 

15-8    19-0 

22-2 

25-4 

28-5 

14 

3-8 

7-6 

11-4 

15-2 

19-0    22-8 

266 

30-4 

24-2 

1 

11 

4-4 

8-9 

13-3 

17-7 

22-2 

26-6 

31-1 

35-5 

39-9 

2 

5-1 

10-1 

15-2 

20-3 

25-3 

30-4 

35-5 

40-6 

45-6 

f 

5-7 

11-4 

17-1 

22-8 

28-5;  34-2 

39-9 

45-0 

51-3 

f 

24 

6-3 

12-7 

19-0 

25-3 

31-7 

38-0 

44-4 

50-7 

570 

1 

7-0 

13-9 

20-9 

27-9 

34-9 

41-8 

48-8 

55-8 

62-7 

a 

3 

7-6 

15-2 

22-8 

30-4 

38-0 

45-6 

53-2 

60-9 

68-4 

4 

a 

34 

8-2 

16-5 

24-7 

33-0 

41-2 

49-4 

57-7 

65-9 

74-2 

4 

34 

8-9 

17-7 

26-6 

35-5 

44-4 

53-2 

62-1 

71-0 

79-9 

1 

31 

9-5 

19-0 

28-5 

38-0 

47-5 

57-0 

66-5 

76-1 

85-6 

3 

4 

10-1 

20-3 

304 

40-6 

50-7 

60-8 

70-9 

81-1 

91-2 

10-8 

21-5 

32-3 

43-1 

53-9 

64-6 

75-4 

86-2 

97-0 

41 

11-4 

22-8 

34-2 

45-6 

57-0 

68-4 

79-9 

91-3 

102-7 

1 

^2 

41 

12-0 

24-1 

36-1 

48-2 

60-2 

72-2 

84-3 

96-3 

108-4 

, 

5 

12-7 

25-3 

38-0 

50-7 

63-4 

76-0 

88-7 

101-4 

114-0 

| 

54 

13-3 

26-6 

39-9 

53-2 

66-5    79-8 

93-1 

106-5 

119-8 

| 

"4 

54 

13-9 

27-9 

41-8 

55-8 

69-7}  83-7 

97-6 

111-5 

125-5 

1 

51 

14-6 

29-1 

43-7 

58-3 

72-9 

87-4 

102-0 

116-6 

131-2 

1 

6 

15-2 

30-4 

456 

60-8 

76-0 

91-2 

106-5 

121-7 

136-9 

I 

14 

5-1 

10-1 

15-2 

20-3 

25-3 

30-4 

35-5 

40-6 

45-6 

I 

2 

6-8 

13-5 

20-3 

27-0 

33-8 

40-6 

47-8 

54-1 

60-8 

I 

3 

10-1 

20-3 

30-4 

40-6 

50-7 

60-8 

70-9 

81-1 

91-2 

1 

4 

13-5 

27-0 

40-6 

54- 

67-6 

81-1 

94-6 

108-1 

121-7 

1 

5 

16-9 

33-8 

50-7 

67-G 

84-5 

101-4 

118-3 

135-2 

152-1 

1 

6 

20-3 

40-6 

608 

81-1 

101-4  121-7 

141-9  162-2  182-5 

^=^=« 

PRACTICAL    TABLES. 
TABLE    III  —  PLAT    IRON. 


Th'k. 

Wid. 

10ft 

lift 

12ft 

13ft 

14ft 

15ft 

IGft 

17ft 

18ft 

inch. 

inch. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

ft 

6 

126-7 

139-4 

152-1 

164-8 

177-4 

190-1 

202-8 

215-4 

228-1 

£ 

1 

25-3 

27-9 

30-4 

33-0 

35-5 

38-0 

40-6 

43-1 

45-6 

1 

u 

31-7 

34-9 

38-0 

41-2 

44-4 

47-5 

50-7 

53-9 

57-0 

1 

li 

38-0 

41-8 

45-6 

59-4 

53-2 

57-0 

60-8 

64-6 

68-4 

1 

11 

44-4 

48-8 

53-2 

57-7 

62-1 

66-5 

71-0 

75-4 

79-9 

I 

2 

50-7 

55-8 

60-8 

65-9 

70-9 

76-0 

81-1 

86-2 

91-2 

1 

24 

57-0 

62-7 

68-4 

74-2 

79:9 

85-5 

91-3 

97-0 

102-7 

I 

2£ 

63-3 

69-7 

76-0 

82-4 

88-7 

95-0 

101-4 

107-7 

114-0 

1 

21 

69-7 

76-7 

83-7 

90-6 

97-6 

104-5 

111-5 

118-5 

125-5 

I 

3 

76-0 

83-6 

91-2 

98-9 

106-5 

114-1 

121-7 

129-3 

136-9 

1 

34 

82-4 

90-6 

98-9 

107-1 

115-3 

123-6 

131-8 

140-0 

148-3 

88-7 

97-6 

106-5 

115-4 

124-2 

133-1 

142-0 

150-8 

159-7 

1 

31 

95-1 

104-6 

114-1 

123-6 

133-1 

142-6 

152-1 

161-6 

171-1 

1 

4 

101-4 

111-5 

121-7 

131-8 

141-9 

152-1 

162-2 

172-4 

182-5 

1 

44 

107-7 

118-5 

129-3 

140-1 

150-8 

161-6 

172-4 

183-2 

193-9 

| 

114-1 

125-5 

136-9 

148-3 

159-7 

171-1 

182-5 

193-9 

205-3 

1 

4| 

120-4 

132-4 

144-5 

156-5 

168-6 

180-6 

192-6 

204-7 

216-7 

1 

5 

126-7 

139-4 

152-1 

164-8 

177-4 

190-1 

202-8 

215-4 

228-1 

1 

54 

133-1 

146-4 

159-7 

173-0 

186-3 

199-6 

212-9 

226-2 

239-5 

| 

139-4 

153-3 

167-3 

181-2 

195-2 

209-2 

223-1 

237-0 

250-9 

1 

51 

145-7 

160-3 

174-9 

189-5 

204-0 

218-6 

233-2 

247-8 

262-3 

1 

6 

152-1 

167-3 

182-5 

197-7 

212-9 

228-1 

243-3 

258-5 

273-7 

1 

H 

50-7 

55-8 

60-8 

65-9 

70-9 

76-0 

81-1 

86-2 

91-2 

1 

2 

67-6 

74-4 

81-1 

87-9    94-6 

101-4 

108-1 

114-9 

121-7 

1 

3 

101-4 

111-5 

121-7 

131-7  141-9 

152-1 

162-2 

172-4 

182-5 

1 

4 

135-2 

148-7 

162-2 

175-7  !  189-3 

202-8 

216-7 

229-8 

243-3 

1 

5 

169-0 

185-9 

202-8 

219-7 

236-6 

253-5 

270-4 

287-3 

304-2 

1 

6 

202-8 

223-1  243-3 

263-6 

283-9 

304-2 

324-4 

344-7 

365-0 

130  PRACTICAL    TABLES. 

The  tables  are  all  calculated  to  the  nearest  tenth  of 
a  pound.  To  the  weights  of  bars  of  Wrought  Iron,  ado 
T|-_th  part  for  bars  of  Soft  Steel  ;  and  from  the  same 
weights  subtract  -Jfth  part  for  bars  of  Cast  Iron. 


Proportional  Breadths  for  hexagonal  or  six-sided  Nut* 
for  Wrought- Iron  Bolts. 

Dia.  of  bolts.    Breadth  of  nuts,   Dia.  of  bolts.    Breadth  of  nut? 
£  £    inch.  1  g-  1  [  j*    inch. 

i  I     "  U  2ft     " 

I  14-"  It  2J       " 

f       IA  "         u       2 A 

H     "  1|  2|      " 

1  If     "    .  If  3 

A'ofe.'—Thc  thickness  of  the  nut  is  equal  the  bolt's  diam 


WEIGHTS    OF    IRON,    COPPER,   ETC.  13) 


Thicknes5s  in  parts  of  an  inch. 

V.**o£w;H-a^H^^ 

^ 

M 

OOlO^CnK/O-'JCnJOO^lCn 

en          en         en          en          en 

s 

i 

p 

Thickness  by  the  wire  gauge. 

^ 

p 

tpcoeo.to.enenqjoi-JOpopoE 

i 

1 

I 

Q 

CJ     ep     .&.     en     en     05^J^J     00     <0     0     •-     10 

tOd5eOodbentOob-J>&.t-idi-q 
»J              *.     00                                                                              Cfl 

10 
o 

s 

1 

CCWh*krffc      in      OiO-sJ      OOOOtDh-      tO 

c3 

CO 

ca 

•n 

t-*(tfc*-OOUii—  'OOtJilOCOOi              H^ 

JO 

g 

Thickness  by  the  wire  gauge. 

SggS3g8£8!g£§S5; 

K3 

s 

p" 

_ 

C5     2      tO                                     tO       Ol                £                C5 

^ 

OD 

01 

3 

ia 

g 

3 

s 

i 

C3 

iss-^^s-^^SSs^s 

£ 

a 

P 

w 


o 

o  *3 

*  > 

§  § 

•a  «TJ 

2  w 

B  g 

JO  *) 

>  2 

5!  >• 

O  P 

w 


o 
g 


Bfl 

W 

B 

H 


Arote. —  JSo.  1  wire  gauge  equal  -j^ths  of  an  inch. 
"    4  "  £  " 

"    7  "  T3(T 

•'  11  "  |  " 

"  16  "  TV         " 

«  22  «  &  « 

The  jrreat  variety  of  thicknesses  into  v,rhich  copper 
is  manufactured,  cause  in  trade  the  weight  to  be  named 
whereby  to  determine  the  thickness  required,  the  unit 
12 


132 


COMPARATIVE    WEIGHTS    OF    BODIES. 


II      It          U         U 

tt     u       u      a 
ft     tt       u      n 


being-  taat  of  a  common  sheet,  so  designated,  viz.,  4  feet 
by  2  feet,  in  Ibs.,  thus  :  — 

A  70    Ib.  plate  is  -j^ths  of  an  inch  in  thickness. 
"  46£  "      "      "    F         "    "      "     "          " 

"23    «      «      « 

"  "4  "     "    " 

"    6    «      «      « 
The  thickness  of  lead  is  also  in  common  determined 
or  understood  by  the  weight  ;  the  unit  being  that  of  a 
square  or  superficial  foot  ;  thus  :  — 

4    Ibs.  lead  is  y^th  of  an  inch  in  thickness. 
6     "      «     "  -i.     "    «     «     «        « 


U 


COMPARATIVE  WEIGHTS   OF  DIFFERENT  BODIES 


Bar  iron  being  1, 

Cast  iron  being  1, 

Cast  iron  =    -95 

Bar  iron 

=  1-07 

Steel         =  1-02 

Steel 

=  1-08 

Copper     =1-16 

Brass 

=  1-16 

Brass         =  1-09 
Lead         =  1-48 

Sr 

=  1-21 
=  1-56 

1.   Suppose  I  have  an  article  of  plate  iron,  the  weight 
of  which  is  728  Ibs.,  but  want  the  same  of  copper,  and 
of  similar  dimensions,  what  will  be  its  weight  ? 
728  x  M6  =844-48  Ibs. 

&  A  model  of  dry  pine,  weighing  32£  Ibs.,  and  in 
which  the  iron  for  its  construction  forms  no  material 
portion  of  the  weight,  what  may  I  anticipate  its  weight 
to  be  in  cast  iron  ? 

32-5  X  16  =  520  Ibs. 

Note.  —  It  frequently  occurs,  in  the  formation  or  construc- 
tion of  models,  that  neither  the  quality  nor  condition  of  the 
timber  can  be  properly  estimated ;  and,  in  such  cases,  it  may 
be  a  near  enough  approximation  to  reckon  15  Ibs.  of  cast  iroi 
Jb  each  Ib.  of  model. 


COPPER    PIPES,    ETC. 


133 


TO    ASCERTAIN    THE    WEIGHTS    OF    PIPES    OF 

VARIOUS     METALS,     AND     ANY    DIAMETER 

REQUIRED. 


Thickness 
:  in  parts  of 
an  inch. 

Wrou»ht 
iron. 

Copper. 

Lead. 

A 

•326 

11£  Ibs.  pJate,    -38 

2   Ibs.lead,  -483 

•As 

•653 

23£  «        «         -76 

>  4     "      "      -967 

A 

•976 

35     "        ".      1-14 

5£  "      "     1-45 

* 

1-3 

46£  «        «       1-52 

8     "      "     1-933 

A 

1-627 

58     «        «       1-9 

9|  "      "     2-417 

A 

1-95 

70     "        "      2-28 

11     "      «     2-9 

A 

2-277 

80£  "       «      2-66 

13     "      "     3-383 

i 

2-6 

93     "        "      3-04 

15    «      "     3-867 

.  —  To  the  interior  diameter  of  the  pipe,  in 
inches,  add  the  thickness  of  the  metal;  multiply  the 
sum  by  the  decimal  numbers  opposite  the  required 
thickness,  and  under  the  metal's  name;  also,  by  the 
length  of  the  pipe  in  feet;  and  the  product  is  the 
weight  of  the  pipe  in  Ibs. 

1.  Required  the  weight  of  a  copper  pipe  whose  in- 
terior diameter  is  1\  inches,  its  length  6£  feet,  and  the 
metal  \  of  an  inch  in  thickness. 

7-5  +  -125  =  7-625  X 1-52  X  6-25  =  72-4  Ibs. 

2.  What  is  the  weight  of  a  leaden  pipe  18<|  feet  in 
length,  3  inches  interior  diameter,  and  the  metal  \  of 
an  inch  in  thickness  ? 

3  +  -25  =  3-25  x  3  867  X  18-5  =  232-5  Ibs. 

Note. —  Weight  of  a  cubic  inch  of 

Lead  equal  -4103  Ib. 

Copper,  sheet       "  -3225  « 

Brass,  do.  "  -3037  " 

Iron,  do.  "  -279  « 

Iron,  cast  «  -263  " 

Tin,  do.  «  -2636  « 

Zinc,  do.  «  -26  « 

Water  «  -03617  « 


1 

134                                          BALLS. 

WEIGHT    OF    CAST    IRON    BALLS. 

Diameter     Weight      Diameter     Weight 

Diameter 

Weight 

in  inches,      in  Ibs.       in  inches,      in  Ibs. 

in  inches. 

in  Ibs. 

2               1-10            6               29-72 

10 

137-71 

24             1-57            64            33-62 

104 

148-28 

2A             2-15             6|            37-80 

io| 

159-40 

2j             2-86             6|             42-35 

wi 

171-05 

3               3-72            7              47-21 

11 

183-29 

34             4-71^,         74            52-47 

114 

19610 

3*            5-80            7J            58-06 

"I 

209  13 

3|             7-26            7|             64-09 

111 

223-40 

4              8-81            8              70-49 

12 

237-94 

44           10-57            84            77-32 

124 

253-13 

4A            12-55             8}            84-56 

12* 

268-97 

4|           14-76            8|            92-24 

12| 

285-37 

5             17-12            9             100-39 

13 

302-41 

64           19-93            94          108-98 

134 

320-80 

5A           22-91             9j           118-06 

13| 

338-81 

5|           26-18             9|           127-63 

13| 

357-93 

1.   What  will  be  the  weight  of  a 

hollow  ball  or  shell 

of  cast  iron,  the  external  diameter 

being  9<| 

,  and  in- 

ternal  diameter  8|  inches  ? 

Opposite  9A  are  118-06,  and 

Opposite  8|  aie    92-24,  subtract 

—  25  82  ibs 

.,  weight  required. 

2.   Requiring  to  remove  a  cast  iron  ball  37-8  Ibs.  in 
weight,  and  in  diameter  6£  inches,  and  replace  it  by 
one  of  lead  of  an  equal  weight,  what  must  be  the 

diameter  of  the  leaden  ball  ? 

Weight  of  lead  to  that  of  cast  iron  =1-56  (see  Table, 

page  132.) 

Then    —  =  3^/176  =  5-f  inches 

the  diameter. 

1-56 

TIMBER    MEASURE. 


135 


TABLES  BY  WHICH  TO  FACILITATE  THE  MEN- 
SURATION  OF   TIMBER. 

1.   Fled  or  Board  Measure. 


Breadth 
n  inches. 

Area  of  a 
lineal  foot. 

Breadth 
in  inches. 

Area  of  a 
lineal  foot. 

Breadth 
in  inches. 

Area  of  a 
lineal  foot. 

A 

•0208 

4 

•3334 

8 

•6667 

| 

•0417 

4i 

•35  i2 

81 

•6875 

| 

•0625 

41 

•375 

8A 

•7084 

1 

•0834 

4| 

•3958 

8f 

•7292 

u 

•1042 

5 

•4167 

9 

•75 

u 

•125 

54 

•4375 

91 

•7708 

if 

•1459 

5j 

•4583 

9$ 

•7917 

2 

•1667 

of 

•4792 

03 

•8125 

2i 

•1875 

6 

•5 

10 

•8334 

2| 

•2084 

6i 

•5208 

101 

•8542 

2| 

•2292 

3 

•5416 

10* 

•875 

3 

•25 

6| 

•5625 

10| 

•8959 

31 

•2708 

7 

•5833 

11 

•9167 

3! 

•2916 

7^ 

•6042 

Hi 

•9375 

3| 

•3125 

7j 

•625 

nJ 

•9583 

7f 

•6458 

llf 

•9792 

Application  and  Use  of  the  Table. 

1.  Required  the  number  of  square  feet  in  a  board  01 
plank  16£  feet  in  length,  and  9|  inches  in  breadth. 

Opposite  9|  is  -8125  x  16-5=  13-4  square  feet. 

2.  A  board  1  foot  2|  inches  in  breadth,  and  21  feet 
in  length ;  what  is  its  superficial  content  in  square  feet  ? 

Opposite  2|  is  -2292,  to  which  add  the  1  foot. 
Then  1-2292  X21  =  25-8  square  feet. 

3.  In  a  board  15^  inches  at  one  end,  9  inches  at  the 
ather,  and  14<|  feet  in  length,  how  many  square  feet  ? 


15-5  4-  9 

Z-  — 124,  or  1-02085  and  1-0208  X  145  = 

12* 


:  14-8  sq.  ft. 


136 


TIMBER    MEASURE. 


Cubic  or  Solid  Measure. 


Mean 
I  girth  in 
inches. 

Cubic  ft.  j 
in  each  ! 
li.ieal  ft.  ! 

Mean 
£  girth  in 
inches. 

Cubic  ft.  j 
in  each  ' 
lineal  ft. 

Mean 
k  g«n'»  in 
inches. 

Cubic  ft. 
in  each 
lineal  ft. 

6 

•25 

14 

1-361 

22 

3-362 

64 

•272 

141 

141 

224 

3-438 

6j 

•294 

4| 

1-46 

22j 

3-516 

61 

•317 

4*| 

1:511 

92* 

3-598 

7 

•340 

5 

1-562 

23 

3-673 

74 

•364 

54 

1-615 

234 

3-754 

7* 

•39 

5$ 

1-668 

tsl 

3-835 

7| 

•417 

54 

1-722 

23| 

3-917 

8 

•4U 

16 

1-777 

24 

4- 

84 

•472 

164 

1-833 

244 

4-084 

gl 

•501 

16j 

1-89 

24.J 

4-168 

8| 

•531 

161 

1-945 

24| 

4-2i>4 

9 

•562 

17 

2-006 

25 

4-34 

94 

•594 

174 

2-066 

251 

4-428 

oT 

•626 

17I 

2-126 

25| 

4-516 

94 

•659 

17| 

2-187 

2^ 

4-605 

10 

•694 

18 

2-25 

26 

4-694 

•73 

18$ 

2-313 

264 

4-785 

10A 

•766 

2-376 

26J 

4-876 

io| 

•803 

18| 

2-442 

26| 

4-969 

11 

•84 

19 

2-506 

27 

5-062 

m 

•878 

194 

2-574 

274 

5-158 

nl 

•918 

m 

2-64 

27£ 

5-252 

ni 

•959 

19| 

2-709 

27| 

5-348 

12 

!• 

20 

2-777 

28 

5-444 

124 
12J 
12| 

1-042 
1-085 
1-129 

20| 

2-898 
2-917 
2-99 

28,^ 
28A 

28| 

5-542 
6-64 
574 

13 

1-174 

21 

3-062 

29 

5-84 

13J 

1-219 

214 

3-136 

291 

5-941 

13A 

1-265 

21A 

3-209 

29A 

6-044, 

13j 

1-313 

2l| 

3-285 

291 

6-146 

CAST    METAL    CYLINDERS. 


137 


In  the  cubic  estimation  of  timber,  custom  has  estab- 
lished the  rule  of  {  the  mean  girth  being  the  side  of 
the  square  considered  as  the  cross  sectional  dimensions* 
hence,  multiply  the  number  of  cubic  feet  per  linea, 
foot,  as  in  the  Table  of  Cubic  Measure,  opposite  the 
i  girth,  and  the  product  is  the  solidity  of  the  given 
dimensions  in  cubic  feet. 

Suppose  the  mean  \  girth  of  a  tree  21$  inches,  and 
its  length  16  feet,  what  are  its  contents  in  cubic  feet  ? 

3-136  X  16  =  50-176  cubic  feet. 


CAST    METAL    CYLINDERS. 

The  cylinders  are  solid,  each  1  foot  in  length. 


Diam. 

Iron. 

Copper. 

Brass. 

Lead. 

inches. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

1 

2-5 

3-0 

2-9 

3-9 

2 

9-8 

12-0 

114 

155 

3 

22-1 

27-0 

25-8 

34-8 

4 

39-3 

47-9 

45-8 

61-9 

5 

614 

74-9 

71-6 

96-7 

6 

884 

107-8 

103-0 

139-3 

7 

120-3 

146-8 

140-2 

189-6 

8 

157-1 

191-7 

183-2 

347-7 

9 

198-8 

242-7 

231-8 

3134 

10 

2454 

299-5 

286-2 

387-0     ! 

CAST    IRON    PIPES. 


This  table  shows  the  weight  of  pipes  1  foot  long,  of 
bores  from  1  inch  to  12  inches  in  diameter,  advancing 
by  £  of  an  inch;  and  of  thicknesses  from  |  of  an 
inch  to  1|  inches,  advancing  by  J  of  an  inch. 


138                              CAST    IRON    PIPES. 

bore. 

i 

1 

i 

8 

1 

i 

1 

11 

li 

in. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

lb». 

Ibs. 

Ibs. 

KM. 

1 

3-1 

5-1 

7-4 

10-0 

12-9 

101 

19-6 

23-5 

27-6 

]4 

3-7 

6-0 

8-6 

11-5 

14-7 

18-3 

22-1 

26-2 

30-7 

n 

4-3 

6-9 

9-8 

13-0 

16-6 

20-4 

24-5 

29-0 

33-7 

M 

4-9 

7-8 

11-1 

14-6 

18-4 

22-6 

27-0 

31-8 

36-8 

a 

5-5 

8-8 

12-3 

1O1 

20-3 

24-7 

29-5 

34-5 

39-9 

2* 

6-1 

9-7 

13-5 

17-6 

22-1 

26-8 

31-9 

37-3 

43-0 

1 

6-7 
7-4 

10-6 
11-5 

14-7 
16-0 

19-2 

20-7 

23-9 
25-7 

28-9 
31-1 

34-4 

36-8 

40-0 
42-8 

46-0 
49-1 

3 

8-0 

12-4 

17-2 

22-2 

27-6 

33-3 

39-3 

45-6 

52«2 

31 

8-6 

12-3 

18-4 

23-8 

29-5 

35-4 

41-7 

48-3 

55-2 

Si 

9-2 

14-2 

19-6 

25-3 

31-3 

37-6 

44-2 

51-1 

58-3 

33 

9-8 

15-2 

20-9 

20-9 

33-1 

39-7 

46-6 

53-8 

61-4 

4 

10-4 

16-1 

22-1 

28-4 

35-0 

41-9 

49-1 

56-6 

64-4 

44 

11-1 

17-1 

23-4 

30-0 

36-9 

44-1 

51-6 

59-4 

67-6 

4I 

11-7 

18-0 

24-5 

31-4 

38-7 

46-2 

54-0 

62-1 

70-6 

4? 

12-3 

18-9 

25-8 

33-0 

40-5 

48-3 

56-5 

64-9 

73-6 

5 

12-9 

19-8 

27-0 

34-5 

42-3 

50-5 

58-9 

67-6 

76-7 

51 

13-5 

20-7 

28-2 

36-1 

44-2 

52-6 

61-4 

70-4 

79-8 

5| 

14-1 

21-6 

29-5 

37-6 

46-0 

54-8 

63-8 

73-2 

82-8 

53 

14-7 

22-6 

30-7 

39-1 

47-9 

56-9 

66-3 

76-0 

85-9 

6 

15-3 

23-5 

31-9 

40-7 

49-7 

59-1 

68-7 

78-7 

88-8 

6| 

16-0 

24-4 

33-1 

42-2 

51-5 

61-2 

71-2 

81-2 

92-0 

6| 

16-6 

25-3 

34-4 

43-7 

53-4 

63-4 

73-4 

84-2 

95-1 

64 

17-2 

202 

35-6 

45-3 

55-2 

65-3 

701 

87-0 

98-2 

7 

17-8 

27-2 

36-8 

46-8 

56-8 

67-7 

78-5 

89-7 

101-2 

7$ 

18-4 

28-1 

38-1 

48-1 

58-9 

69-8 

81-0 

92*5 

104-2 

3 

19-0 

29-0 

39-1 

49-9 

60-7 

72-0 

83-5 

95-3 

1074 

H 

19-6 

29-7 

40-5 

51-4 

62-6 

74-1 

85-9 

98-0 

110-5 

8 

20-0 

30-8 

41-7 

52-9 

64-4 

76-2 

88-4 

100-8 

113-5 

81 

209 

31-7 

43-0 

54-5 

66-3 

78-4 

90-8 

103-5 

11O6 

8£ 

21-7 

32-9 

44-4 

56-2 

68-3 

80-8 

93-5 

106-5 

•119-9 

83 

22-1 

33-6 

45-4 

57-5 

70-0 

82-7 

95-7 

109-1 

122-7 

9 

22-7 

34-5 

46-6 

59-1 

71-8 

84-8 

98-2 

111-8 

125-8 

9i 

23-3 

35-4 

47-9 

60-6 

73-6 

87-0 

100-6 

114-6 

128-9 

9i 

23-9 

304 

49-1 

62-1 

75-5 

89-1 

103-1 

117-4 

131-9 

91 

24-8 

37-3 

50-3 

63-7 

77-3 

91-3 

105-5 

120-1 

1350 

10 

25-2 

38-2 

51-5 

65-2 

79-2 

93-4    108-0  !  122-8 

138-1 

10} 

25-8 

39-1 

52-8 

66-7 

81-0 

95-6 

110-4    125-6!  141-1 

io| 

26-4 

40-0 

54-0 

68-3 

82-8 

97-7 

112-9    128-4 

144-2 

io| 

27-0 

41-0 

55-2 

69-8 

84-7 

99-9 

115-4'  131-2 

147-3 

11 

27-6 

41-9 

56-5 

71-3 

805     102-0!  117-8    133-9 

150-3 

111 

28-2 

42-8 

57-7 

72-9 

88-4     104-2  i  120-3    136-7 

153-4 

111 

28-8 

43-7 

58-9 

74-4 

90-2     1003  !  122-7    139-4 

1504 

113 

29-5 

44-6 

60-1 

75-9 

92-0     108-5    125-2    142-2 

159-5 

<2 

30-1 

45-6 

61-4 

77-5 

93-6  i  110-6  i  127-6    145-0 

162-6 

,  —  ,  ___  .  j 

DEGREES  OF  HEAT. 


139 


TABLE    FOR    COMPOSITIONS    OF    BRASS,    &C. 

3  parts  copper,  0  tin,  I  zinc,  for  yellow  brass. 


0  • 

1 

1      " 

for  Spelter, 
for  lathe  bushes. 

1 

1     « 

still  harder. 

h     " 
0    " 
0    " 

for  bearings  of  shafts, 
for  harder  bearings, 
fit  for  pulley  blocks, 
fit  for  wheels. 

a 

0    « 

gun  metal 

The  effect  of  different  degrees  of  heat  on  different 
bodies,  according  to  Fahrenheit's  scale,  are  shown 
below:  — 

Degrees 

Cast  iron  thoroughly  melted, 20577 

Cast  iron  begins  to  melt, 17U77 

Greatest  heat  of  a  common  smith's  forge,      .     .     .     173117 

Flint  glass  furnace,  strongest  heat, 158*17 

Welding  heat  of  iron,  greatest, 131"27 

Swedish  copper  melts,     ....     4 45H7 

Brass  melts ^ 3807 

Iron  red-hot  in  the  twilight, 884 

Heat  of  a  common  lire, 790 

Iron  bright  red  in  the  dark, 752 

Zinc  melts,    , • 700 

Mercury  boils, 672 

Lead  melts, £94 

The  surface  of  polished  steel  becomes  uniformly  a 

deep  blue, 58C 

The  surface  of  polished  steel  becomes  a  pale  straw 

color, 4(10 

A  mixture  of  3  tin  and  2  lead  melts, 33^ 


CENTRE, 

In  a  general  sense,  denotes  a  point  equally  remote 
from  the  extremes  of  a  line,  surface,  or  solid. 


140  CENTRES. 


CENTRE    OF    ATTRACTION 

Of  a  body,  is  that  point  into  which,  if  all  its  matter 
is  collected,  its  action  upon  any  remote  particle  would 
still  be  the  same. 


CENTRE    OF    EQUILIBRIUM 

Is  the  same, -in  respect  to  bodies  immersed  in  a  fluid 
as  the  centre  of  gravity  is  to  bodies  in  free  space. 

CENTRE    OF    FRICTION 

Is  that  point  in  the  base  of  a  body  on  which  it  re- 
volves, into  which,  if  the  whole  surface  of  the  base 
and  the  mass  of  the  body  were,  collected,  and  made  to 
revolve  about  the  centre  of  the  base  of  the  given  body, 
the  angular  velocity  destroyed  by  its  friction  would  be 
equal  to  the  angular  velocity  destroyed  in  the  given 
body  by  its  friction  in  the  same  time. 

CENTRE    OF    GRAVITY 

Of  any  body,  or  system  of  bodies,  is  that  point  upon 
which  the  body,  or  system  of  bodies,  acted  upon  only 
by  the  force  of  gravity,  will  balance  itself  in  all  posi- 
tions ;  hence  it  follows,  that,  if  a  line  or  plane,  passing 
through  the  centre  of  gravity,  be  supported,  the  body 
or  system  will  be  also  supported. 

CENTRE    OF    GYRATION 

Is  that  point  into  which,  if  the  whole  mass  were 
collected,  a  given  force,  applied  at  a  given  distance, 
would  produce  the  same  angular  velocity  in  the  same 
time  as  if  the  bodies  were  disposed  at  their  respective 
distances. 

This  point  differs  from  the  Centre  of  Oscillation  only 
m  this,  that,  in  the  latter  case,  the  motion  is  produced 


COHESION.  141 

by  the  gravity  of  the  body ;  but,  in  the  former,  the  body 
is  put  in  motion  by  some  other  force,  acting  at  one 
place  only. 

COHESION 

Is  that  species  of  attraction  which,  uniting  particle 
to  particle,  retains  together  th  *  component  parts  of  the 
same  mass ;  being  thus  distin  ruished  from  adhesion,  or 
that  species  of  attraction  which  takes  place  between 
the  surfaces  of  similar  or  dissimilar  bodies.  The 
absolute  cohesion  of  solids  is  measured  by  the  force 
necessary  to  pull  them  asunder.  Thus,  if  a  rod  of  iron 
be  suspended  in  a  vertical  position,  having  weight 
attached  to  its  lower  extremity  till  the  rod  breaks,  the 
whole  weight  attached  to  the  rod,  at  the  time  of  frac- 
ture, will  be  the  measure  of  its  cohesive  force,  or  abso- 
lute cohesion. 

The  particles  of  solid  bodies,  in  their  natural  state, 
are  arranged  in  such  a  manner,  that  they  are  in  equi- 
librium in  respect  to  the  forces  which  operate  on  them ; 
therefore,  when  any  new  force  is  applied,  it  is  evident 
that  the  equilibrium  will  be  destroyed,  and  that  the 
particles  will  move  among  themselves  till  it  be  restored. 
When  the  new  force  is  applied  to  pull  the  body  asunder, 
the  body  becomes  longer  in  the  direction  of  the  force, 
which  is  called  the  extension ;  and  its  area,  at  right 
angles  to  the  direction  of  the  force,  contracts.  When 
the  force  is  applied  to  compress  the  body,  it  becomes 
shorter  in  the  direction  of  the  force,  which  is  called  the 
compression ;  and  the  area  of  its  section,  at  right  angles 
to  the  force,  expands.  In  either  case,  a  part  of  the 
heat,  or  any  fluid  that  occupies  the  pores  or  interstices 
of  the  body,  before  the  new  force  was  made  to  act 
upon  it,  will  be  expelled. 

CASE-HARDENING. 

The  hardness  and  polish  of  steel  may  be  united,  ic 
a  certain  degree,  with  the  firmness  and  cheapness  of 


14*2  CASE-IIAUDENKN'G. 

malleable  iron,  by  what  is  called  case-hardening;  an 
operation  much  practised,  and  of  considerable  use. 

It  is  a  superficial  conversion  of  iron  into  steel,  and 
only  differs  from  cementation  in  being  carried  on  for  a 
shorter  time.  Some  artists  pretend  to  great  secrets  in 
the  practice  of  this  art,  using  saltpetre,  sal-ammoniac, 
and  other  fanciful  ingredients,  to  which  they  attribute 
their  success.  But  it  is  now  an  established  fact,  that 
the  greatest  effect  may  be  produced  by  a  perfectly 
tight  box,  and  animal  carbon  alone. 

The  goods  intended  to  be  case-hardened,  being  pre- 
viously finished,  with  the  exception  of  polishing,  are 
stratified  with  animal  carbon,  and  the  box  containing 
them  luted  with  equal  parts  of  sand  and  clay.  They 
are  then  placed  in  the  fire,  and  kept  at  a  light  red  heat 
for  half  an  hour,  when  the  contents  of  the  box  are 
emptied  into  water.  Delicate  articles,  like  files,  may 
be  preserved  by  a  saturated  solution  of  common  salt, 
with  any  vegetable  mucilage,  to  give  it  a  pulpy  con- 
sistence! The  carbon  here  spoken  of  is  nothing:  more 
than  any  animal  matter,  such  as  horns,  hoofs,  skins,  or 
leather,  just  sufficiently  burned  to  admit  of  beim*  re- 
duced to  powder.  The  box  is  commonly  made  of  iron, 
but  the  use  of  it,  for  occasional  case-hardening  upon  a 
small  scale,  may  easily  be  dispensed  with,  as  it  will 
answer  the  same  end  to  envelop  the  articles  with  the 
composition  above  directed  to  be  used  as  a  lute,  drying 
it  gradually  before  it  is  exposed  to  a  red  heat,  other- 
wise it  will  probably  crack.  It  is  easy  to  infer,  that 
the  depth  of  the  steel,  induced  by  case-hardening,  will 
vary  with  the  time  the  operation  is  continued.  It  may 
be  varied  from  one  hour  to  four,  according  to  the  depth 
of  steel  required.  In  one  hour,  it  will  scarcely  be  the 
thickness  of  a  fourpence,  and  therefore  may  be  re- 
moved by  violent  abrasion,  though  sufficient  to  answer 
well  for  fire-irons,  and  a  multitude  of  other  utensils,  in 
the  common  usage  of  which  its  hardness  prevents  its 
being  easily  scratched,  and  its  polish  preserved  by 
friction  with  so  soft  a  material  as  leather. 


STEAM-ENGINES.  143 

To  estimate,  by  means  of  an  indicator,  t.e  amount  of 
effective  power  produced  by  a  steam-engine. 

Rule.  —  Multiply  the  area  of  the  piston  in  square 
inches  by  the  average  force  of  the  steam  in  Ibs.,  and  by 
the  velocity  of  the  piston  in  feet  per  minute ;  divide  the 
product  by  33,OuO,  and  y7^ths  of  the  quotient  equal  the 
effective  power. 

Ex.  Suppose  an  engine  with  a  cylinder  of  37£  inches 
diameter,  a  stroke  of  7  feet,  and  making  17  revolutions 
per  minute,  or  238  feet  velocity,  and  the  average  indi- 
cated pressure  of  the  steam  1O73  Ibs.  per  square  inch , 
required  the  effective  power. 

Area  =  1104-^87  inches  x  16-73  Ibs.,  x  238  feet. 
33000 

133.%  y  7 

= —  93-282  horses'  power. 

10 

To  determine,  the  proper  velocity  for  the  piston  of  a. 
steam-engine. 

Rule.  —  Multiply  the  logarithm  of  the  nth  part  of  the 
stroke  at  which  the  steam  is  cut  off  by  2-3,  and  to  the 
product  of  which  add  7.  Multiply  the  sum  by  the  dis- 
tance in  feet  the  piston  has  travelled  when  the  steam  is 
cut  off,  and  120  times  the  square  root  of  the  product 
equal  the  proper  velocity  for  the  piston  in  feet  per 
minute. 

Ex.  Let  the  steam  be  cut  oft  in  an  8-feet  stroke 
when  the  piston  has  travelled  4th  of  the  length ;  re- 
quired its  proper  velocity. 

Logarithm  of  4  =  0-60206 
Multiplied  by  2-3 

1-384738 
To  which  add        -7 

2-084738 
2 

V  4-169476  =  2-04  x  120  =  245  feet,  velocity 
1 3  per  minute 


144 


STEAM-ENGINES. 


Table  of  Approximate  Velocities  for  the  Pistons  oj  Steam* 
Engines. 


Condensing  Engines. 

Non-condensing  Engines. 

Length 
of  stroke 

Velocity  in 
feet  per 

Number  of 
revolutions 

Length 
of  stroke 

Velocity  in 
feet  per 

Number  of 
revolutions 

in  feet. 

minute. 

per  nun. 

in  feet. 

minute. 

per  nun. 

2 

160 

40 

4 

186 

62 

2£ 

177A 

35k 

2 

200 

50 

3 

192 

32 

a 

2124 

42£ 

203 

29 

21 

217J 

3D«| 

4 

214 

26} 

3 

222 

37 

24j 

31 

231 

33 

5^ 

230 

23 

4 

236 

29A 

Q 

236A 

21A 

4£ 

243 

27 

6 

240 

20 

5 

247^ 

21-^ 

7 

245 

171 

51 

253 

23 

S 

2.56 

16 

6 

264 

22 

Of  the  Parallel  Motion  in  a  Steam-Engine. 

When  the  power  from  the  piston  is  communicated 
by  means  of  a  beam  or  lever  moving  upon  an  axis,  the 
parallel  motion  becomes  a  very  important  portion  of  the 
machine ;  for  then  it  forms  the  link  of  connection,  and 
by  its  properties  renders  the  action  of  alternate  circular 
motion,  and  reciprocating  vertical  motion,  mutually 
agreeable,  thereby  properly  insuring  to  the  piston  rod 
a  truly  direct  line  to  that  of  the  cylinder;  but  to  effect 
this,  the  greatest  degree  of  exactitude  of  the  various 
parts  is  required,  otherwise  extra  friction  is  created,  and 
the  effective  powe*  of  the  engine  proportionately  dimin- 
ished. 


PARALLEL  MOTIONS. 


145 


Table  by  which  to  determine  the  various  Distances  of  tht 
Movable  Points  in  a  Parallel  Motion. 


15  j 


2  0 

1  4| 

0  10  = 

0  6J 

0  4 


is; 

iP 

o   53 


4     6 


1  4 

0  11> 

£-Zi 

4  8g 

3  71 

2  9 
2  1 

1  U 


3  10 

3  0 

2  3| 

1  9.1 

1  41 

1  0 


3 
33 

31. 

41 

4|  j  0    81 


4  11 

3  3 

2  6j 

2  Oi 


o 


5  4 

4  4 

3  6 

3  2| 

2  3 

1  9 

1  4| 

i  0'; 

0  9g 


4  6| 

3  9 

3  0^ 

2  6 

2  0 

1  7 

1  3 

0  ll.i 


5 
4 
4 

3 

9 

1     5l 


91 


« 


6  0^ 

5  63 

4  3 

3  6| 

2  11J 

2  53 

??! 


6  3 

5  35 

4  6 

3  9| 

Q       Ol 

1  If 

2  25 

1  10 

J__6_ 

5  6| 

4  9 

*  si 

2  107 
2    5| 
2    04 


5  9. 

5  0 

4  3 

3  8 

3  1 

2  8 

2  3 

1  10 


li 


6  0^ 
5  3 
4  6£ 
3  11 
3  3| 
2  10J 


6  34 
5  6 
4  94 
4  2 
3 
3 
2 


7g 
« 


6  61 

5  9 

5  Oi 

4  5 
3  10| 

3  4 
2  10$ 

2  6 

6  8) 
6  0 

5  2\ 

4  7| 
4  1 

3  6^ 
3  1 


5*1 


140  LOGARITHMS. 


LOGARITHMS. 


LOGARITHMS  literally  signify  ratios  of  numbers ;  hence 
Logarithmic  Tables  may  be  various,  but  those  ir.  com- 
mon use  for  the  facilitating1  of  arithmetical  operations 
generally  are  of  the  following  corresponding  progres- 
sions, viz. : — 

Arithmetical,  0,    1,    2,       3,     &c.,  or  series  oflogaritmns. 
Geometrical,  1,  10,  100,  1000,  &c.,  or  ratio  of  numbers. 

And  thus  it  may  be  perceived,  that  if  the  log.  of  JO  be 
J,  the  log.  of  any  number  less  than  10  must  consist 
wholly  of  decimals,  because  increasing  by  a  decimal 
ratio.  Again;  if  the  log.  of  100  be  2,  the  log.  of  any 
intermediate  number  between  10  and  100  must  be  1. 
with  so  many  decimals  annexed ;  and  in  like  manner, 
the  log.  of  any  intermediate  number  between  100  and 
1000,  must  be  2,  with  decimals  annexed  proportionally, 
as  before. 


APPLICATION    AND    UTILITY    OF    COMMON    LOGA- 
RITHMIC   TABLES. 

The  whole  numbers  of  the  series  of  logarithms,  aa 
I,  2,  3,  &c.,  are  called  the  indices,  or  characteristics 
of  the  logarithm,  and  which  must  be  added  to  the 
logarithm  obtained  by  the  Table,  in  proportion  to  the 
number  of  figures  contained  in  the  given  sum.  Thus, 
suppose  the  logarithm  be  reqaired  for  a  sum  of  only  two 
figures,  the  index  is  1  ;  if  of  three  figures,  the  index  is  2; 
and  if  of  four  figures,  the  index  is  3,  &c. ;  being  always 
a  number  less  by  unity  than  the  number  of  figures  the 
given  sum  contains. 


LOGARITHMS.  14? 

Ex.  The  index  of  8  is  0,  because  it  is  less  than  10 

The  index  of  80  is  1,  because  it  is  less  than  100. 

The  index  of  800  is  2,  because  it  is  less  than  1000. 

The  index  of  8000  is  3,  because  it  is  less  than 
10,000,  &c. 

The  index  of  a  decimal  is  always  the  number  which 
denotes  the  significant  figure  from  the  decimal  point, 
and  is  marked  with  the  sign,  thus,  —  ,  to  distinguish  it 
a  whole  number. 


Ex.  The  index  of  -32549  is  —  1,  because  the  first  sig- 
nificant figure  is  the  first  decimal. 

The  index  of  -032549  is  —  2,  because  the  first  signi- 
ficant figure  is  the  second  decimal. 

The  index  of  -0032549  is  —  3,  because  the  first  sig- 
nificant figure  is  the  third  decimal,  &c.,  of  any  other 
sum. 

If  the  given  sum  for  which  the  logarithm  is  required 
contains  or  consists  of  both  integers  and  decimals,  the 
index  is  determined  by  the  integer  part,  without  having 
any  regard  to  the  other. 

1.  To  Jind  the  logarithm  of  any  whole  number  under 
100. 

Look  for  the  number  under  N  in  the  first  page  of 
any  Logarithmic  Table  ;  then  immediately  on  the  right 
of  it  is  the  logarithm  required,  with  ts  proper  index. 
Thus  the  log.  of  64  is  1-806180,  and  the  log.  of  72  is 
1-857332. 

2.  To  Jind  the  logarithm  of  any  number  between  100 
and  1000,  or  any  sum  not  exceeding  4  figures. 

Find  the  first  three  figures  in  the  left-hand  column 
of  the  page  under  N,  in  which  the  number  is  situated, 
and  the  fourth  figure,  at  the  top  or  bottom  of  the 
page  ;  then  the  logarithm  directly  under  the  fourth 
figure,  and  in  a  line  with  the  three  figures  in  the  column 
on  the  1  3ft,  with  its  proper  index,  is  the  logarithm  re- 


1 48  LOGARITHMS. 

quired.  Thus,  the  log.  of  450  is  2-653213-  and  the  log 
of  7464  is  3-872972.  Or,  the  log.  of  378-5  is  2-57806$ 
and  that  of  -7854  is  —  1-895091. 

3.   To  find  ibt  number  indicated  by  a  given  logarithm 

Look  for  the  decimal  part  of  the  given  logarithm  in 
the  different  columns,  and  if  it  cannot  be  found  exactly, 
take  the  next  less.  Then  under  N  in  the  left-hand 
column,  and  in  a  line  with  the  logarithm  found,  are 
three  figures  of  the  number  required,  and  on  the  top  of 
the  column  in  which  the  found  logarithm  stands  is  one 
figure  more;  place  the  decimal  point  as  indicated  by 
the  logarithmic  index,  which  determines  the  sum,  prop- 
erly valued,  as  required. 

If  the  logarithm  cannot  be  found  exactly  ir.  the 
Tables,  subtract  from  it  the  next  less  that  can  be  found, 
and  divide  the  remainder  by  the  tabular  difference ;  the 
quotient  will  be  the  rest  of  the  figures  of  the  given 
number,  which,  being  annexed  to  the  tabular  number 
already  found,  is  the  proper  number  required. 

Ex.  Required  the  number  answering  to  ihe  loga- 
rithm 3-233568. 

Given  logarithm       .     .     .     .  =  3-233568 
Next  leas  is  the  log.  of    1712  =  3-233604 

Remainder  64 

Tab.  n;«r  —  553  and  —  =  -25 

253 
Hence  the  number  required  =1712-25. 

For  practical  purposes  in  mechanics,  logarithms  are 
seldom  resorted  to,  unless  for  the  raising  of  the  powers 
of  numbers  or  extraction  of  their  roots.  These  opera- 
tions, when  tables  are  at  hand,  they  very  nmch  facili- 
tate ;  involution,  or  the  raising  of  powers,  being  per- 
formed simply  by  multiplication,  and  evolution,  or  the 
extraction  of  roots,  by  division,  as  in  simple  arithmetic. 


LOGARITHMS.  149 

Ex.  1.    Required  the  square  or  second  power  of 

25791. 

Log.  of  25-791  =  1-411468 

Multiplied  by  2  the  power  required. 

Logarithm    2  822936  indicated   number   or   square  re- 
quired =  665-115. 

Ex.2.  What  is  the  cube  of  30-7146? 

Logarithm        =  1-487345 

Multiplied  by  3  the  power  required. 

Logarithm    4-462035  indicated  number  or  cube  required 

=  28975-7. 

Ex.  3.  Required  the  square  root  of  365. 

2-56^293 

Log.  = —  =  l-28?14b  indicated  number  or  root  =  19-105. 

2 

Ex.  4.  Find  the  cube  root  of  12345. 

4-091491 
Log.  =  — =  1-363830  indi-?atwi  number  or  root 


150 


LOGAK1THMS. 


Table  of  Logarithms  Jrorn  1  to  100. 


N. 

Log. 

N. 

Log. 

N. 

Log. 

N. 

Log. 

1 

0-000000 

26 

1-414973 

51 

1-707570 

re 

1-880814 

2 

0-301030 

27 

1-431364 

52 

1-716003 

",7 

1-886491 

3 

0-477121 

28 

1-447158 

53 

1-724276 

73 

1-892095 

4 

0-602060 

29 

1-462398 

54 

1-732394 

79 

1-897627 

5 

0-698970 

30 

1-477121 

55 

1-740363 

80 

1-903090 

6 

0-778151 

31 

1  491362 

56 

1-748188 

81 

1-908485 

7 

0-845098 

32 

1-505150 

57 

1-755875 

82 

1-913814 

8 

0-903090 

33 

1-518514 

58 

1  763428 

83 

1-919078 

9 

0-954243 

34 

1-531479 

59 

1-770852 

84 

1-924279 

10 

1-000000 

35 

1-544068 

60 

1-778151 

85 

1-929419 

11 

1-041393 

36 

1-556303 

61 

1-785330 

86 

1-934498 

12 

1-079181 

37 

1-568202 

62 

1-792392 

87 

1-939519 

13 

1-113943 

38 

1-579784 

63 

1-799341 

88 

1-944483 

14 

1-146128 

39 

1-591065 

64 

1-806180 

89 

1-949390 

15 

1-176091 

40 

1-602060 

65 

1-812913 

90 

1-954243 

16 

1-204120 

41 

1-612784 

66 

1-819544 

91 

1-959041 

17 

1-230449 

42 

1-623249 

67 

1-826075 

92 

1-963788 

18 

1  255273 

43 

1-633468 

68 

1-832509 

93 

1-968483 

19 

1-278754 

44 

1-643453 

69 

1-838849 

94 

1-973128 

20 

1-301030 

45 

1-653213 

70 

1-845098 

95 

1-977724 

21 

1-322219 

46 

1-662758 

71 

1-851258 

96 

1-982271 

22 

1-342423 

47 

1-672098 

72 

l-&>7332 

97 

1-986772 

23 

1-361728 

48 

1-681241 

73 

1-863323 

98 

1-991226 

24 

1-380211 

49 

1-693196 

74 

1-869232 

99 

1-995635 

25 

1-397940 

50 

1-698970 

75 

1-875061 

100 

2-000000 

Note.  —  The  best  Tables  of  Logarithms  are  those  by  Taylor, 
Gardiner,  Hutton,  Babbage,  and  Gail  let.  The  smaller  work* 
are  those  by  Lalande,  Hassler,  Renaud,  Christison,  and  Wai 
lace,  and  those  published  in  the  "  Library  of  Useful  Kuowiecge. 


WATER   IN    PIPES. 


TABLE • 


-WATER    IN    PIPES. 


This  table  shows  the  quantity  and  weight  of  water 
contained  in  one  fathom  of  length  of  pipes  of  different 
bores  from  1  inch  to  12  inches  in  diameter,  advancing 
by  half  inch.  The  weight  of  a  cubic  foot  of  water  ia 
taken  at  1000  ounces  avoirdupois,  and  the  imperial 
gallon  at  10  Ibs. 


Diameter 
in  inches. 

Quantity  in 
cubic  inches. 

Quantity  in 
imperial  gallons. 

Weight  in  Ibs 
avoirdupois. 

i 

14-14 

0-051 

0-51 

1 

56-55 

0-205 

2-05 

J£ 

12723 

0-460 

4-60 

2 

226-19 

0-818 

8-18 

ft 

35343 

1-278 

12-78 

3 

508-94 

1  841 

1841 

34 

692-72 

2-506 

25-06 

4 

904-78 

3272 

32-72 

4£ 

1145-11 

4-142 

41-42 

5 

1413-72 

5-113 

51-13 

5* 

1710-60 

6-187 

61-87 

6 

2035-75 

7-363 

73-63 

6£ 

2389-18 

8-641 

86-41 

7 

2770-88 

10-022 

100-22 

*J 

3180-86 

11-505 

115-05 

8 

3619-11 

13-090 

130-90 

8| 

4085-64 

14-777 

14777 

9 

4580-44 

16-567 

16567 

»* 

5103-52 

18-459 

184-59 

10 

5654-87 

20-453 

204-53 

10£ 

6234  49 

22-550 

225-50 

11 

6842-39 

24748 

247-48 

ii| 

7478-56 

27-049 

270-49 

12 

8143-01 

29-452 

294-52 

152     CHANGES    IN    THE    STRUCTURE    OF    IRON. 


CHANGES    INDUCED    IN    THE    STRUCTURE    OP 
IRON    SUBSEQUENT    TO    MANUFACTURE. 

The  important  purposes  to  which  iron  is  applied  have 
a.ways  rendered  it  a  subject  of  peculiar  interest ;  and 
at  no  period  has  its  importance  been  so  general  and 
extensive  as  at  the  present  time,  when  its  application  is 
almost  daily  extending,  and  there  is  scarcely  any  thing 
connected  with  the  arts  to  .which,  either  directly  or 
indirectly,  it  does  not  in  some  degree  contribute.  My 
object  is  to  point  out  some  peculiarities  in  the  habitudes 
.  of  iron,  which  appear  to  have  almost  wholly  escaped 
the  attention  of  scientific  men,  and  which,  although  in 
some  degree  known  to  practical  mechanics,  have  been 
generally  considered  by  them  as  isolated  facts,  and  not 
regarded  as  the  results  of  a  general  law.  The  circum- 
stances, however,  well  deserv^,the  attention  of  scientific 
men,  on  account  of  the  very  important  consequences  to 
which  they  lead. 

The  two  great  distinctions,  which  exist  in  malleable 
wrought  iron,  are  known  by  the  names  of  red-short  and 
cold-short  qualities.  The  former  of  these  comprises 
the  tough,  fibrous  iron,  which  generally  possesses  con- 
siderable strength  when  cold  ;  the  latter  shows  a  bright, 
crystallized  fracture,  and  is  very  brittle  when  cold,  but 
works  ductile  while  hot  These  distinctions  are  per- 
fectly well  known  to  all  those  who  are  conversant  with 
the  qualities  of  iron  ;  but  it  is  not  generally  known  that 
there  are  several  ways  by  which  the  tough,  red-short 
iron  becomes  rapidly  converted  into  the  crystallized; 
and  that,  by  this  change,  its  strength  is  diminished  to  a 
very  great  extent.  The  importance  which  attaches  to 
this  subject  will  not  be  denied.  The  principal  causes 
which  produce  this  change  are  percussion,  heat,  and 
magnetism ;  and  it  is  doubtful  whether  either  of  these 
means  will  produce  this  effect;  and  there  appear  strong 
reasons  for  supposing  that,  generally,  they  are  all  in 


CHANGES    IN    THE    STRUCTURE    OF    IRON       153 

some  degree  concerned  in  the  production  of  the  ob- 
served results.  The  most  common  exemplification  or* 
the  effect  of  heat,  in  crystallizing  fibrous  iron,  is  by 
breaking  a  wrouo-ht-iron  furnace-bar ;  which,  whatever 
quality  it  was  of  in  the  first  instance,  will,  in  a  short 
time,  invariably  be  converted  into  crystallized  iron; 
and,  by  heating,  and  rapidly  cooling  by  quenching  with 
water  a  few  times,  any  piece  of  wrought  iron,  the  same 
effect  may  be  far  more  speedily  produced.  In  these 
cases,  we  have  at  least  two  of  the  above  causes  in 
operation  —  heat  and  magnetism.  In  every  instance 
of  heating  iron  to  a  very  high  temperature,  it  under- 
goes a  change  in  its  electric  or  magnetic  condition; 
for,  at  very  high  temperatures,  iron  entirely  loses  its 
magnetic  powers,  which  return,  as  it  gradually  cools  to 
a  lower  temperature.  In  the  case  of  quenching  the 
heated  iron  with  water,  we  have  a  still  more  decisive 
assistance  from  the  electric  and  magnetic  forces ;  for 
Sir  Humphrey  Davy  long  since  pointed  out,  that  all 
cases  of  vaporization  produced  negative  electricity  in 
the  bodies  in  contact  with  the  vapor ;  —  a  fact  which 
has  lately  excited  a  good  deal  of  attention,  in  conse- 
.quence  of  the  discovery  of  large  quantities  of  negative 
electricity  in  effluent  steam.  These  results,  however, 
are  practically  of  but  little  consequence ;  but  the  effects 
of  percussion  are  at  once  various,  extensive,  and  ot 
high  importance.  We  shall  trace  these  effects  under 
several  different  circumstances. 

In  the  manufacture  of  some  descriptions  of  ham- 
mered iron,  the  bar  is  first  rolled  into  shape,  and  then 
one-half  the  length  of  the  bar  is  heated  in  a  furnace, 
and  immediately  taken  to  the  tilt-hammer  and  ham- 
mered ;  and  the  other  end  of  the  bar  is  then  heated 
and  hammered  in  the  same  manner.  In  order  to  avoid 
tiny  unevenness  in  the  bar,  or  any  difference  in  its 
color  where  the  two  distinct  operations  have  terminated, 
the  workman  frequently  gives  the  bar  a  few  blows 
with  the  hammer  on  that  part  which  he  first  operated 
upon.  That  part  of  the  bar  has,  however,  by  this  time, 


154      CHANGES    IN    THE    STRUCTURE    OF    IRON. 

become  comparatively  cold;  and,  if  this  cooling1  pro- 
cess has  proceeded  too  far  when  it  receives  this  addi- 
tional hammering1,  that  part  of  the  bar  immediately 
becomes  crystallized,  and  so  extremely  brittle  that  it 
will  break  to  pieces  by  merely  throwing  it  on  the 
ground,  though  all  the  rest  of  the  bar  will  exhibit  the 
best  and  toughest  quality  imaginable.  This  change, 
therefore,  has  been  produced  by  percussion  as  the 
primary  agent.  We  here  see  the  effects  of  percussion 
in  a  very  instructive  form.  And  it  must  be  observed, 
that  it  is  not  the  excess  of  hammering  which  produces 
the  effect,  but  the  absence  of  a  sufficient  degree  of 
heat  at  the  time  the  hammering  takes  place ;  and  the 
evil  may  probably  be  all  produced  by  five  or  six  blows 
of  the  hammer,  if  the  bar  happens  to  be  of  a  small 
size.  In  this  case,  we  witness  the  combined  effects  of 
percussion,  heat,  and  magnetism.  When  the  bar  is 
hammered  at  the  proper  temperature,  no  such  crystal- 
lization takes  place,  because  the  bar  is  insensible  to 
magnetism ;  but,  as  soon  as  the  bar  becomes  of  that 
lower  degree  of  temperature  at  which  it  can  be  affected 
by  magnetism,  the  effect  of  the  blows  it  receives  is  tc 
produce  magnetic  induction ;  and  that  magnetic  in- 
duction, and  consequent  polarity  of  its  particles,  when 
assisted  by  further  vibrations  from  additional  percussion, 
produces  a  crystallized  texture.  For  it  is  perfectly 
well  known  that,  in  soft  iron,  magnetism  can  be  almost 
instantaneously  produced  by  percussion  ;  and  it  is 
probable  that,  the  higher  the  temperature  of  the  bar  at 
the  time  it  receives  the  magnetism,  the  more  likely 
will  it  be  to  allow  of  that  rearrangement  of  its  mole- 
cules vvhich  would  constitute  the  crystallization  of  the 
iron.  It  is  not  difficult  to  produce  the  same  effects  by 
repeated  blows  from  a  hand-hammer  on  small  bars  of 
iron;  but  it  appears  to  depend  upon  something  peculiai 
in  the  blow,  which,  to  produce  the  effect,  must  occasion 
B.  complete  vibration  among  the  particles  in  the  neigh 
borhood  of  the  part  which  is  struck.  And  it  is  re 
niarkable  that  the  effects  of  the  biows,  in  all  cases, 


CHANGES    IN    THE    STRUCTURE    OF   IRON       155 

ueem  to  be  confined  within  certain  limited  distances 
of  the  spot  which  receives  the  strokes. 

Dr.  Wollaston  first  pointed  out  that  the  forms  in 
which  native  iron  is  disposed  to  break,  are  tl.ose  of 
the  regular  octahedron  and  tetrahedron,  or  rhomboid, 
consisting  of  these  forms  combined.  The  tough  and 
fibrous  character  of  wrought  iron  is  entirely  produced 
by  art ;  and  we  see,  in  these  changes  that  have  been 
described,  an  effort  at  returning  to  the  natural  and 
primal  form;  —  the  crystalline  structure,  in  fact,  being 
the  natural  state  of  a  large  number  of  metals ;  —  and 
Sir  Humphrey  Davy  has  shown,  that  all  those  which 
are  fusible  by  ordinary  means  assume  the  form  of 
regular  crystals  by  slow  cooling.  The  general  con- 
clusion, to  which  these  remarks  lead  us,  appears  to 
leave  no  doubt  that  there  is  a  constant  tendency  in 
wrought  iron,  under  certain  circumstances,  to  return  to 
the  crystallized  state ;  but  that  this  crystallization  is 
not  necessarily  dependent  upon  time  for  its  develop- 
ment, but  is  determined  solely  by  other  circumstances, 
of  which  the  principal  is,  undoubtedly,  vibration.  Heat, 
within  certain  limits,  though  greatly  assisting  the 
rapidity  of  the  change,  is  certainly  not  essential  to  it ; 
but  magnetism,  induced  either  by  percussion  or  other- 
wise, is  an  essential  accompaniment  of  the  phenomena 
attending  the  change. 


14 


156        STRENGTH    OF    JOURNALS    OF    SHAFTS. 


STRENGTH   *)F    JOURNALS    OF    SHAFTS. 

Mr.  Buchanan's  rule  is  —  The  cube  root  of  the 
vveignt  in  cwts.  is  nearly  equal  to  the  diameter  of  the 
journal;  —  it  being  prudent  to  make  the  journal  a  little 
more  than  less,  and  to  make  a  due  allowance  for  wear- 
ing. 

JEx.  What  is  the  diameter  of  a  journal  of  a  water- 
wheel  shaft,  13  feet  long,  the  weight  of  the  wheel  being 
15  tons  ? 

By  Mr.  B.'s  rule, 

V  15  X  20  =  6-7,  or  7  inches  diameter. 
By  Mr.  Tredgold's  rule, 

3360 

Weight  in  the  middle. X  13  =  873  3A/873  =  9A  inches 

500 
diameter. 


Weight  equally  distributed,  33600  X  13  =  436800 


=  7-65  inches.  10 


To  resist  Torsion  or  Twisting. 

It  is  obvious  that  the  strength  of  revolving  shafts* 
are  directly  as  the  cubes  of  their  diameters  and  revqlu- 
tions;  and  inversely,  as  the  resistance  they  have  to 
overcome. 

Mr.  Robertson  Buchanan,  in  his  essay  on  the  Strength 
of  Shafts,  gives  the  following  data,  deduced  from  several 
experiments,  viz.:  That  the  fly-wheel  shaft  of  a  50- 
horse-power  engine,  at  50  revolutions  per  minute,  re- 
quires to  be  7£  inches  diameter ;  and  therefore,  the  cube 
of  this  diameter,  which  is  —  421  -875,  seives  as  a  multi- 

*  Shafts,  here,  are  understood  as  the  journals  of  shafts,  the  bodies 
of  shafts  being  generally  made  square. 


STRENGTH  OF  JOURNALS  OF  SHAFTS.    157 

plier  to  all  other  shafts  in  the  same  proportion ;  and, 
taking  this  as  a  standard,  he  gives  the  following  multi- 
pliers, viz. :  — 

For  the  shaft  of  a  steam-engine,  water-wheel,  or  any  shaft 

connected  with  a  first  power, 400 

For  shafts  in  inside  of  mills,  to  drive  smaller  machinery,  or 

connected  with  the  shafts  above, 200 

For  the  small  shafts  of  a  mill  or   machinery, 100 

From  the  foregoing,  the  following  rule  is  derived, 
viz. :  The  number  of  horses'  power  a  shaft  is  equal  to, 
is  directly  as  the  cube  of  the  diameter  and  number  of 
revolutions ;  and  inversely,  as  the  above  multipliers. 

Ex.  1.  When  the  fly-wheel  shaft  of  a  45-horse-power 
steam-engine  makes  90  revolutions  per  minute,  what  is 
the  diameter  of  the  journal  ? 

4.5  v  400  Q 

A         =  200  3V200  =  5T8o-  inches  diameter. 
90 

Ex.  2.  The  velocity  of  a  shaft  is  80  revolutions  per 
minute,  and  its  diameter  is  3  inches ;  what  is  its  power  ? 

33x80 

=  5-4  horses7  power. 

400 

Ex.  3.  What  will  be  the  diameter  of  the  shaft  in  the 
first  example,  when  used  as  a  shaft  of  the  second  multi- 
plier ?  * 

5-8  3^45  x  200       .  6     . 

=  4-64,  or       =  4^77  inches  diameter 

1-25  90 

The  following  is  a  table  of  the  diameters  of  shafts, 
oeing  the  first  movers,  or  having  400  for  their  multi- 
pliers. 

*  The  diameters  of  the  second  movers  will  be  found  by  dividing  tht 
nunbers  in  the  Table  by  1-25,  and  the  diameters  of  the  third  movers, 
>y  dividing  the  numbers  by  1-56. 


158 


DIAMETERS    OF    THE 


II 
T 

Revolutions. 

10 

15 

20 

25 

30  |   35 

40 

45 

50 

55 

Inches  Diameter. 

5.5 

4-8 

4-5 

4- 

37 

3-H 

35 

3-3 

32'  3-1 

5 
6 

5-9 
6-3 

5-1 

5-5 

4-7 
5- 

44 

41 

3-9 

37 

36 

35 

3-3 
3-6 

46 

44 

41 

4- 

38 

3-7 

7 

6-6 

5-8 

5-2 
5-5 

4-9 

46 

44 

4-2 

4- 

3-9 

37 

8- 
9 
10, 
12 

6!) 

6- 
6-3 

51 

4-8 

46 

4-4 
45 

42 

41 

4- 
41 
42 
4-6 
47 
5- 

72 

5-7 
5-9 
63 

5-5 
56 

5- 

4-8 

4-4 
46 

42 

7-4 
7-9 

6-6 
6-9 

52 

4-9 

47 

44 

5-8 
6-2 

5-6 

5-4 

5-2 

5- 

4-8 
5- 

14 
16 

8-3 

72 

67 

5-9 

5-6 

5-4 

5-2 

8-7 

76 

71 

66 

61 

5-8 

56 

5-4 

5-2 

18 
20 
25 

9- 
93 
10- 

7-9 

75 

7-7 

7- 

66 

62 

5-8 

5-6 

5-4 

52 
54 

8-1 
8-5 

72 

6-8 

64 

5-9 

57 

56 

8- 

7-4 

71 

6-8 

6-3 

6- 

5-9 

56 

30 

10-7 

9-3 

8-4 
8-9 

7-9 

74 

71 

74 

6-9 

67 

65 

63 
65 
67 

68 
73 

35 

40 

114 
117 
12- 
12-6 

9-8 
10-5 
10-6 

8-4 

7-9 

71 

6-9 
72 

66 

9-3 

9-7 
10- 

8-8 

8-3 

7-8 

7-4 

6-9 

45 

50 

92 

8-7 

8-1 

7-6 

7-4 

7- 

11- 

9-3 

9- 

8-5 

8- 

7-8 

7-4 

55 
60 

13-4 

11-4 

10-4 

9-8 

9-1 

8-8 

8-4 

8- 

7-5 

7-4 
7-6 

136 

12- 

10-8 

10- 

9-3 

9- 

8-6 

8-2 

7-7 

JOURNALS    OF    FIRST    MOVERS.                159 

I 

1  ' 

T 

5 

Revo  utions. 

- 

60 

65     70 

75 

80 

85  |  90   |  95     100 

1C5 

Inches  Diameter. 

3- 

2-9 

2-9 

2-8 

2-7 

27 

26 

2-6 

26 

2-5 

33 

32 

3-1 

3- 

3- 

29 

2-9 

2-8 

2-8 

2-7 

6 

7 
8 

35 

35 

3-4 

33 

32 

32 

3- 

3- 

2-9 

2-9 

36 
3-9 

36 

35 

34 

34 

33 
35 

3-3 
3-4 

32 

3-1 

3-1 

3-8 

3-7 

3-6 

3-5 

3-4 

33 

32 

9 

10 
12 

4- 

3-8 

3-7 

37 

3-6 

3-6 

3-5 

3-5 

3-4 

3-3 

41 
44 

4- 

3-9 

3-8 

3-7 

3-7 

36 

3-6 

35 

34 

43 

42 

41 

4 
42 

3-9 

3-8 

3-8 

3-7 

3-6 

14 
16 

18 
20 
25 
30 

45 

4.4 

44 
46 

4-3 

41 

4- 

4- 

3-9 

3-8 

4-8 
5- 
52 
5-5 

47 

45 

44 

4-4 
4-5 

43 
44 

42 

4-1 

4- 

4-9 

48 

4-7 

46 

4-3 

4-2 

4-2 

51 

5- 

4-8 

4-6 

46 

4-5 

4-5 

44 

4-4 
46 

54 

53 

5-2 

5-1 

4-9 

4-8 

4-7 

4-6 

5-9 
63 

5-8 
61 

5-7 

56 

5-5 

5-3 

5-2 
5-4 
5-7 

51 

5- 

4-9 

35 

5-9 

5-7 

5-6 
5-9 

55 

5-8 
6- 

5-3 

5-2 

5-2 

40 
15 

6-6 
6-7 

6-4 

6-2 
6-4 

6- 

5-6 

56 

5-5 

6-5 
69 

6-2 

61 

5-9 

5-8 

5-7 

56 

5-8 

50 

7-2 

6-8 

66 

6-5 

6-4 

6-2 

6- 

5-9 

55 
60 

7-3 

7-2 

7- 

6-7 

66 

65 

6-3 

62 

6-1 
6-4 

6- 

~ei 

7-4, 

7-3 

72 

6-9 

6-8 

6-8 

67 

66 

14* 

10 J  STRENGTH    OF    WHEELS. 

It  is  ?i  well  known  fact,  that  a  cast  iron  rod  will  BUS- 
tain  more  torsional  pressure  than  a  malleable  iron  rod 
of  the  same  dimensions ;  that  is,  a  malleable  iron  rod 
will  be  twisted  by  a  less  weight  than  what  is  required 
to  wrench  a  cast  iron  rod  of  the  same  dimensions. 

When  the  strength  of  malleable  is  less  than  that 
of  cast  iron  to  resist  torsion,  it  is  stronger  than  cast  iron 
to  resist  lateral  pressure,  and  that  is  in  proportion  as  9 
is  to  14. 

From  the  foregoing,  it  is  easy  for  the  millwright  to 
make  his  shafts  of  the  iron  best  suited  to  overcome  the 
resistance  to  which  they  will  be  subject,  and  the  pro- 
portion of  the  diameters  of  their  journals,  according  to 
the  iron  of  which  they  are  made. 

Ex.  What  will  be  the  diameter  of  a  malleable  iron 
journal  to  sustain  an  equal  weight  with  a  cast  iron  jour- 
nal of  7  inches  diameter. 

73=343. 

A*  14  :  $13  : :  9 :220£  j  now  3V  220  5  =  6-04  inches  diameter. 


STRENGTH    OF    WHEELS. 

The  arms  of  wheels  are  as  levers  fixed  at  one  end, 
and  loaded  at  the  other;  and,  consequently,  the  greatest 
strain  is  upon  the  end  of  the  arm  next  the  axle.  For  that 
reason,  all  arms  of  wheels  should  be  strongest  at  that 
part,  and  tapering  toward  the  rim. 

The  rule  for  the  breadtb  and  thickness  of  arms,  ac- 
cording to  their  length  and  number  in  the  wheel,  is  as 
follows :  Multiply  the  power  or  weight  acting  at  the  end 
of  the  arm  by  the  cube  of  its  Jength ;  the  product  of 
which,  divided  by  !2(j56  times  the  number  of  arms  mul- 
tiplied by  the  deflection,  will  give  the  breadth,  and 
cube  of  the  depth. 

Ex.  Suppose  the  force  acting  at  the  circumference 
of  a  spur-wheel  to  be  1600  Ibs.,  the  radius  of  wheel  6 


STRENGTH    OF    WHEELS.  161 

feet,  and  number  of  arms  8,  and  let  the  deflection  not 
exceed  T\yth  of  an  inch. 

— X  GS     =  1G3  =  breadth  and  cube  of  the  deptli 
2656  X  8  x  1 

Let  the  breadth  be  2-5  inches ;  therefore,  —  =  65-2  j 

2-5 

which  is  equal  to  the  cube  of  the  depth.  Now  the 
cube  root  of  65-2  is  nearly  4-03  inches :  this,  conse- 
quently, is  the  depth  or  dimension  of  each  arm  in  tho 
direction  of  the  force. 

Note.  __  When  the  depth  at  the  rim  is  intended  to  be  hall 
that  of  the  axes,  use  1640  as  a  divisor  instead  of  2656. 

The  teeth  are  as  beams,  or  cantilevers,  fixed  at  one  end  and 
loaded  at  the  other.  The  rule  applying  directly  to  them  where 
the  length  of  the  beam  is  the  length  of  the  teeth,  and  the  depth 
the  thickness  of  the  teeth.  For  the  better  explanation  of  the 
rule,  the  following  example  is  given. 

Ex.  The  greatest  power  acting  at  the  pitch  line  ot 
the  wheel  is  6000  Ibs.,  and  the  thickness  of  the  teeth 
1£  inch,  the  length  of  the  teeth  being  0-25  feet;  it  is 
required  to  determine  the  breadth  of  the  teeth. 

6000X0*5^  1500  =  ^  .ncheg> the  breadth  required< 
212  X  1-52      477 

In  order  that  the  teeth  may  be  capable  of  offering  a 
sufficient  resistance  after  being  worn  by  friction,  the 
breadth  thus  found  should  be  doubled ;  therefore,  ir  the 
above  example,  the  breadth  should  be  64,  or  say  6£ 
inches. 

The  following  data  are  gleaned  from  experiments, 
which  are,  therefore,  valuable,  and  of  much  use  to  the 
practical  mechanic. 

Rule.  _  Multiply  the  breadth  of  the  teeth  by  the 
square  of  the  thickness,  and  divide  the  product  by  the 
length ;  the  quotient  will  be  the  proportional  strength 
in  horses'  power,  with  a  velocity  of  2-27  feet  per  second. 


STRENGTH    OF    WHEELS. 


Ex.  What  is  the  power  of  a  wheel,  the  teeth  of 
which  are  6  inches  broad,  J -5  inch  thick,  and  1-8  inch 
long,  and  revolving  at  the  velocity  of  3  feet  per  second  5 

'b2  x  6      13'5 

= =  7-5,  strength  at  2-27  feet  per  second ;  then 

1-8          1-8 

7*5  X  3 

2-27  : 7-5  : :  3  = =  991  horses'  power. 

2'27 

Hide.  —  The  pitch  is  found  by  multiplying  the  thick- 
ness by  2*1,  and  the  length  is  found  by  multiplying  the 
thickness  by  1-2. 

Ex.  The  thickness  being  2  inches,  what  is  the  pitch 
4nd  length  ? 

2x  2-1=4-2,  pitch. 
2x  1-2  =  2-4,  length 

Note.  —  The  breadth  of  the  teeth,  as  commonly  executed  by 
the  best  mechanics,  seems  to  be  from  about  twice  to  thrice  the 
pitch. 


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CIRCUMFERENCES    OF    CIRCLES.  163 


TABLES 

OF    THE 

CIRCUMFERENCES  OF  CIRCLES, 

TO    THE 

NEAREST    FRACTION    OF   PRACTICAL    MEASUREMENT, 

ALSO    THE 

AREAS   OF   CIRCLES 

IN    INCHES    AND    DECIMAL    PARTS,    LIKEWISE    IN 

FEET    AND    DECIMAL    PARTS,    AS    MAY    BE 

REQUIRED. 


Rules  that  may  render  the  following  Talks  more  gen» 
erally  useful. 

1.  Any  of  the  areas  in  inches  multiplied  by  '04328, 
or  the  areas  in  feet  multiplied  by  0-232,  the  product  is 
the  number  of  imperial  gallons  at  1  foot  in  depth. 

2.  Any  of  the  areas  in  feet  multiplied  by  -03704,  the 
product  equal  the  number  of  cubic  yards  at  1  foot  in 
depth. 

3.  The  area  of  a  circle  in  inches  multiplied  by  the 
length  or  thickness  in  inches,  and  by  -263,  the  product 
equal  the  weight  in  Ibs.  of  cast  iron. 


oe.  _  The  French  cubic  metre,  or  unit  of  solid  measure, 
equal  35-31716  English  cubic  feet.  Also  the  litre,  or  unit  for 
measures  of  capacity,  equal  61-028  English  cubic  inches,  or 
about  -463  of  an  imperial  gallon, 


lOl                           CIRCUMFERENCES   AND 

1 

Dia.  in 
inch. 

Circuin. 
in  iiidi. 

Area  in 
q.  inch. 

-icieof 

Dia.  in 

inch. 

Cir.  in 
ft.    in. 

Area  in 
q.  inch. 

Ar.in 

sq.  ft. 

TV 

•196 

•0030 

•0554 

3m. 

9| 

7-068 

2| 

i 

•392 

•0122 

•1107 

3J 

9| 

7-669 

2| 

T5 

•589 

•0276 

•1661 

3^ 

10^ 

8-295 

2& 

£ 

•785 

•0490 

•2115 

3^ 

10| 

8-946 

3  in. 

A 

•981 

•0767 

•2669 

3d 

11 

9-621 

3& 

1 

1-178 

•1104 

•3223 

3| 

Hi 

10-320 

H 

T7? 

1-374 

•1503 

•3771 

31 

ill 

11044 

3| 

£ 

1-570 

•1963 

•4331 

3^ 

12^ 

11-793 

3y7B 

& 
* 

1-767 
1-963 

•2485 
•3068 

•4995 
•5438 

4  in. 

o^ 

12-566 
13-364 
14-186 

•0879 
•0935 
0993 

TF 

2-159 

•3712 

•6093 

4| 

]| 

15-033 

•1052 

£ 

2-356 

•441? 

•66-46 

$ 

2| 

15-904 
16-800 

•1113 
•1176 

TF 

2-552 

•5185 

•7200 

4| 

2 

17-720 

•1240 

£ 

2-748 

•6013 

•7754 

4^ 

3i 

18-665 

•1306 

i£ 

2-945 

•6903 

•8308 

5  in. 

3I 

19635 

•1374 

20-629 

•1444 

lin. 

34 

•7854 

7 

4 

4 

21-647 

•1515 

*^8 

° 

53 

4? 

22-690 

•1588 

H 

34 

•9940 

B&32" 

3 

5! 

23-758 

•1663 

U 

3& 

1-227 

1  in. 

^i 

5| 

24-850 

•1739 

C  «feo  HN 

44 

1-484 
1-767 

•A 
iA 

af 

6 

6| 

25-967 
27-108 

•1817 
•1897 

6m. 

65 

28-274 

•1979 

It 

5J 

2-074 

irV 

7| 

29-464 

•2062 

If 

5£ 

2-405 

i  9 

64 

7| 

30-679 

2147 

1| 

2-761 

Hi 

6i 

8 

31-919 
33-183 

•2234 
•2322 

2  in 

6J 

3-141 

11 

Gl 

83 

34-471 
35-784 

•2412 
•2504 

2J 

61 

3-546 

ii 

fii 

94 

37-122 

•2598 

2£ 

7 

3-976 

2  in. 

7  in. 

10 

38-484 

•2(593 

! 

2f 

7f 

4-430 

2J 

74 

7} 

10| 

39-871 
41-282 

2791 
•2889 

2£ 

7| 

4-908 

2y3^ 

7f 

ll| 

42-718 

•2990 

81 

gi 

5-412 

2-A» 

71 

Hi 

44-178 

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21 

8| 

5-939 

2fV 

ll 

2    Of 

45-663 
47-173 

•3196 
•3299 

2& 

9 

6-491 

2y9F 

7| 

2    Of 

48-707 

•3409 

AREAS    OF    CIRCLES. 


165 


Dia.  in 

Cir.  in 

Area  in 

Area  in! 

Dia.  in 

Cir.  in 

Area  in 

Area  in 

inch. 

ft.  in. 

sq.  inch. 

,q.  ft. 

inch. 

ft.  in. 

sq.  inch. 

sq.  ft. 

Sin. 

2  H 

50-265 

•3518 

13m. 

3  4| 

132-732 

•9291 

8$ 

2  1A 

51-848 

•3629 

134 

3  54 

135-297 

•9470 

ft 

2  \l 

53-456 

•3741 

3  58 

137-886 

•9642 

8j 

2  24 

55-088 

•3856 

131 

3  6 

140-500 

•9835 

& 

2  2g 

56-745 

•3972 

13A 

3  6§ 

143-139 

1-0019 

8! 

2  3 

58-426 

•4089 

131 

3  6| 

145-802 

1-0206 

8; 

2  3§ 

60-132 

•4209 

13| 

3  71 

148-489 

1-0294 

8i 

2  3£ 

61-862 

•4330 

13* 

3  7A 

151-201 

1-0584 

9  in. 

2  44 

63-617 

•4453 

14  in. 

3  11 

153-938 

1-0775 

9^ 

2  4f 

65-396 

•4577 

14| 

3  8f 

156-699 

1-0968 

94 

2  5 

67-200 

•4704 

144 

3  8f 

159-485 

•1193 

9$ 

2  5| 

69-029 

•4832 

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3  91 

162-295 

•1360 

4 

2  5| 

70-882 

•4961 

14  A 

3  9j| 

165-130 

•1569 

9l 

2  64 

72-759 

•5093 

14* 

3  9? 

167-989 

•1749 

9| 

2  6f 

74-662 

•5226 

14$ 

3  10J 

170-873 

•1961 

9| 

2  7 

76-588 

•5361 

14J 

3  103 

173-782 

•2164 

10  in. 

2  7| 

78-540 

•5497 

15  in. 

3  11£ 

176-715 

•2370 

10£ 

2  7l 

80-515 

•5636 

15£ 

3  ll| 

179-672 

•2577 

10^ 

2  8| 

82-516 

•5776 

15^ 

3  111 

182-654 

•2735 

id 

2  8^ 

84-540 

•5917 

158 

4  Oj 

185-661 

•2996 

10* 

2  8^ 

86-590 

•6061 

15A 

4  Of 

188-692 

•3208 

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88-664 

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191-748 

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90-762 

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4  1£ 

194-828 

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197-933 

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11  in. 

2  10A 

95-033 

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16  in. 

4  24 

201-062 

•4074 

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2  10J 

97-205 

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4  2| 

204-216 

•4295 

n 

2  114 

99-402 

•6958 

164 

4  3 

207-394 

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101-623 

•7143 

161 

4  3§ 

210-597 

1-4741 

nj 

3  Of 

103-869 

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164 

4  3| 

213-825 

1-4967 

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3  OA 

106-139 

•7429 

1GJ 

4  44 

217-077 

1-5195 

n 

3  01 

108-434 

•7590 

16| 

4  4g 

220-353 

1-64-24 

•*i 

' 

3  ij 

110-753 

•7752 

16| 

4  5 

223-654 

1-5655 

12  in. 

3  1| 

113-097 

•7916 

17  in. 

4  5§ 

226-980 

1-5888 

I6'  A 

3  2 

115-466 

•8082 

17£ 

4  53 

230-330 

1-6123 

124 

3  2£ 

117-859 

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174 

4  6| 

233-705 

1-6359 

12$ 

3  2| 

120-276 

•8419 

171 

4  6^ 

237-104 

1-6597 

12A 

3  34 

122-718 

•8590 

17i 

240-528 

1-6836 

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3  3| 

125-185 

•8762 

17| 

4  7| 

243-977 

1-7078 

12* 

3  4 

127-676 

•8937 

17| 

4  7| 

247-450 

1-7321 

12| 

3  4j| 

130-192 

•9113 

2f 

4  8| 

250-947 

1-7566 

166           CIRCUMFERENCES  AND 

Dia.  in 
inch. 

Cir.  in 
ft.  in. 

Area  in 
sq.  inch. 

Area  in 
sq.  ft. 

Dia.  in 
inch. 

Cir.  in 
ft.  in. 

Area  in 
sq.  inch. 

Area  in 
sq.  ft. 

18 

4  8£ 

254-469 

1-7812 

23 

6  OJ 

415-476 

2-8903 

18| 

4  8f 

258-Olfi 

1-8061 

23£ 

6  0| 

420-004 

2-9100 

18.4 

4  94 

261-587 

1-8311 

23^ 

6  1 

424-557 

2-9518 

181 

4  9| 

265-182 

1  -8562 

23| 

6  1| 

429-135 

2  9937 

UU 

4  10| 

268-803 

1-8816 

23A 

6  1| 

433-737 

3-0129 

181 

4  10A 

272-447 

1-9071 

23| 

6  2j 

438-363 

3-0261 

18| 

4  10§ 

276-117 

1-9328 

23| 

6  2| 

443-014 

3-0722 

18| 

4  llj 

279-811 

1-9586 

23$ 

6  3 

447-690 

3-1081 

19 

4  11| 

283-529 

1-9847 

2  0 

6  3f 

452-390 

3^1418 

! 

19ft 

5  0 

287-272 

1-99-11 

2  Oi 

6  4} 

461-864 

3-2075 

1 

19* 

5  OA 

291-039 

2-0371 

2  OA 

6  4g 

471-436 

3-2731 

I 

19f 

5  Oi 

294-831 

2-0637 

2  03 

6  5i| 

481-106 

3-3410 

| 

19£ 

5  14 

298-648 

2-0904 

2  1 

6  6j 

490-875 

3-4081 

19§ 

5  if 

302-489 

2-1172 

2  1| 

6  1\ 

500-741 

3-4775 

1 

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5  2 

306-355 

2-1443 

2  l| 

6  8^ 

510-706 

3-5468 

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5  2f 

310-245 

2-1716 

2  if 

6  8£ 

520-769 

3-6101 

20 

5  2g 

314-160 

2-1990 

2  2 

6  9| 

530-930 

3-6870 

20£ 

5  34 

318099 

2-2265 

2  2^ 

6  10| 

541.-189 

3-7583 

204 

5  3g 

322i*53 

2-2543 

2  C4 

6  114 

551-547 

3-8302 

20f 

5  4 

326-04 

2-2822 

2  2| 

7  0 

562-002 

3-9042 

2o| 

5  4| 

330-6  I 

2-3103 

2  3 

1  Of 

572-556 

3-9761 

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5  4| 

334-101 

2-3386 

2  3^ 

7  If 

583-208 

4-0500 

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5  5f 

338-163 

2-3670 

2  3A 

7  2| 

593-958 

4-1241 

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5  5£ 

342-250 

2-3956 

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7  3£ 

604-807 

4-2000 

21 

5  5£ 

346-361 

2-4244 

2  4 

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615-753 

4-2760 

2U 

5  6f 

350-497 

2-4533 

2  44 

7  41 

626-798 

4-3521 

214 

5  6f 

351-G.V7 

2-4824 

2  4| 

7  6A 

637-941 

4-4302 

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5  7| 

358-841 

2-5117 

2  4| 

7  64 

649-182 

4-5083 

21£ 

5  7I 

363-051 

2-5-112 

2  5 

7  7 

660-521 

4-5861 

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5  7| 

367-284 

2-5708 

2  54 

7  7S 

671-958 

4-6665 

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5  84 

371-543 

2-6007 

2  5A 

7  8f 

683-494 

4-7467 

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5  8| 

375-826 

2-6306 

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7  9j 

695-128 

4-8274 

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5  9£ 

380-133 

2-6608 

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7  10| 

706-860 

4-9081 

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384-465 

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718-690 

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730-618 

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402-038 

2-7980 

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766-992  '5-3264 

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410-972 

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AREAS  OF  CIRCLES.            167 

Dia.  in 
ft.  in. 

Cir.  in 
ft.  in. 

Area  in 
sq.  inch. 

Area  in 
sq.  ft. 

Dia.  in 
ft.  in. 

Cir.  in 
ft.  in. 

Area  in 

sq.  in. 

Area  in 

sq.  ft- 

2  8 

8  4£ 

804-249 

5-5850 

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10  m 

1385-44 

9-6212 

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8  5£ 

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1369-00 

9-5061 

4  3|  13  6j  2103-35 

14-606 

' 

15 

CIRCUMFERENCES    AND 


Dia.  in 

Cir.  in 

Area  in 

Area  in 

Dia.  in 

Cir.  in 

Area  in 

Area  in 

ft.  in. 

ft.  in. 

sq.  inch. 

sq.  ft. 

ft.  in. 

ft.  in. 

sq.  inch. 

sq.  ft.  j 

4  4 

13  7g 

2123-72 

,  4-74-0 

5  2 

16  2i 

3019-07 

20-965 

4  44 

13  8^ 

2144-19 

>  4-890 

5  24 

16  3j; 

3043-47 

21-135 

4  4'| 

13  8i 

2164-75 

13  OS-? 

5  2A 

16   4; 

30(57-96 

21-305 

4  42 

13  9f 

2185-42 

15176 

5  2| 

16  6J 

3092-56 

21-476 

4  5 

13  10£ 

2206-18 

o  3l\) 

5  3 

16  5| 

3117-25 

21-647 

4  54 

13  114 

2227-05 

15-165 

5  34 

16  64 

314204 

21-819 

4  5j 

14  o 

2248-01 

15-611 

5  3A 

16  7A 

316692 

21-992 

4  5^ 

U  f-jf 

2269-06 

15-757 

5  3| 

16  8| 

3191-91 

22-166 

4  6 

14  1 

2290-22 

15-90* 

5  4 

16  9 

3216-99 

22-333 

4  64 

14  2g 

2311-48 

16-051 

5  4£ 

16  9| 

3242-17 

22-515 

4  6j 

14  3i 

2332-83 

16-200 

5  4j 

16  I0§ 

3267-46 

22-621 

4  64 

14  4 

2354-28 

16-349 

5  4J 

16  111 

3292-83 

22-866 

4  7 

14  4| 

2375-83 

16-498 

5  5 

17  0| 

3318-31 

23-043 

4  7| 

14  5£ 

2397-48 

l/i-649 

5  54 

17  t)| 

3343-88 

23-221 

4  g 

14  6f 

2419-22 

16-800 

5  5A 

17  1| 

3369-56 

23-330 

4  § 

H  7i 

2441-07 

16-951 

5  5| 

17  2| 

3395-33 

23-578 

4  8 

14  7£ 

24  ^3-01 

f7-104 

5  6 

17  38 

3421  -°20 

23-758 

4  8j 

14  8| 

2485-05 

17-257 

5  64 

17  4! 

3447-16 

23-938 

4  8£ 

14  9  A 

2507-19 

17-411 

5  6| 

17  42 

3473-23 

24-119 

4  8| 

14  10J 

2529-42 

17565 

5  l| 

17  5f 

3199-39 

24-301 

4  9 

14  11 

2551-76 

17-720 

5  7 

17  6A  |352,3-66 

24-483 

4  94 

14  llg 

2574-19 

17-876 

5  74 

17  74 

3552-01 

24-666 

4  9£ 

15  0{j 

2596-72 

18-033 

5  7A 

17  8 

357847 

24-U50 

4  9$ 

15  If 

261935 

18-139 

5  7| 

17  8| 

3605-03 

25-034 

4  10 

15   4 

2642-08 

18-3t7 

5  8 

17  9g 

3631-68 

25-220 

4  10J 

15   f 

2664-91 

18-506 

5  84 

17  108 

9656-44 

25-405 

4  10J 

15  8 

2687-83 

18-665 

5  8j 

17  11| 

3685-29 

25-692 

4  10-f 

15  4£ 

2710-85 

18-825 

5  8| 

17  11£ 

3712-24 

25-779 

4  11 

15  5^ 

2733-97 

18-985 

5  9 

18  0| 

3739-28 

25-964 

4  114 

15  6J 

2757-19 

19-147 

5  94 

18  1A 

3766-43 

26-155 

4  111 

15  62 

2780-51 

19-309 

5  9l 

18  24 

3793-67 

26-3-14 

4  llf 

15  7| 

2803-92 

19-471 

JLJ! 

18  3| 

3821-02 

26  534 

5  0 

?5  8} 

2827-44 

19-635 

j  10 

18  31 

3848-46 

26-725, 

5  01 

15  9} 

2851-05 

19-798 

5  104 

18  4 

3875-99 

26-916 

5  0£ 

15  10 

2874-76 

19-963 

5  10| 

18  5A 

3903-63  27-108 

5  Of 

15  10| 

2898-56 

20-128 

5  10| 

18  64 

3931-36  J27-301 

5  1 

15  111  2922-47 

20-294 

5  11 

18  7 

3959-20  27-494 

5  1.4 

16  0§  2946-47 

20-461 

5  114 

18  7| 

3987-13 

27-688 

5  1A 

16  ij 

2970-57 

20-629 

5  111 

18  8f 

4015-16 

27-883 

5  If 

16  l| 

2994-77 

20-797 

5  11| 

18  9| 

4045-28 

28-078 

AREAS    OF   CIRCLES. 


169 


Dia.  in 

Cir.  in 

Area  in 

Area  in  |Dia.  in 

Cir.  in 

Area  in 

Area  in 

ft.  in. 

ft.  in. 

sq.  inch. 

sq.  ft. 

ft.  in. 

ft.  in. 

sq.  in. 

sq.  ft. 

6  0 

18  104 

4071-51 

28-274 

6  6 

20  5 

4778-37 

33-183 

6  0| 

18  104 

4099-83 

28-471  1 

6  64 

20  53 

4809-05 

33396 

c  o| 

18  111 

4128-25 

28-668 

6  6] 

20  6A 

4839-83 

33-619 

6  0| 

19  Oj 

415677 

28-866 

6  6| 

20  7| 

4870-70 

33-824 

6   1 
6   \i 
6   U 

19  ll 

19  2| 
19  24 

4185-39 
4214-11 
4242-92 

29-065 
29-264 
29-466 

6  7 
6  71 
6  7A 

20  8£ 
20  8l 
20  9} 

4901-6834-039 
4932-7534-255 
4963-9234-471 

6   if 

19  3£ 

4271-83 

29-665 

6  7| 

20  10^ 

4995-19 

34-688 

6  2 

19  4£ 

4300-85 

29-867 

6  8 

20  114 

5026-26 

34-906 

6  24 

19  54, 

4329-95 

30-069 

6  84 

21  0|l5058-02|35  125 

6  2j 

19  6 

4359-16 

30-271 

6  8| 

21  02 

5089-51:  135-344 

6  2f 

19  6| 

438847 

30-475 

6  8| 

21  l| 

5121-2435-564 

6  3 

19  7c 

4417-87 

30-679 

6  9 

21  2|'  5  153-00  35-784 

6  34. 

19  8$ 

4447-37 

30-884 

6  94 

21  345184-8636-006 

6  3£ 

19  9i 

4476-97 

31-090 

6  9j 

21  4  5216-82;36-227 

6  3| 

19  9£ 

4506-67 

31-296 

6  9| 

21  4| 

5248-87 

36-450 

6  4 

19  10| 

453647 

31-503 

6  10 

21  5£ 

5281-02 

36-674 

6  44 

19  llj 

4566-36 

31-710 

6  104 

21  6|  5313-27  36-897 

6  4j 

"20  04, 

4596-35 

31-919 

6  10A 

21  7|  5345-62  37-122 

6  4| 

20  \\ 

4626-44 

32-114 

6  10| 

21  7^  5378-07  37-347 

6  5 

20  if 

4656-63 

32-337 

6  11 

21  815410-62  37-573 

6  54 

20  2f 

4686-92 

32-548 

6  114 

21  9j  5443-26  37-700 

6  5| 

20  & 

4717-30 

32-759 

6  ll| 

21  10J  5476-00  38-027 

6  flj 

20  4| 

4747-79 

32-970 

6  11| 

21  11  5508-8438-256 

170                         CIRCUMFERENCES   AND 

Dianrr  in 
ft.  and  in. 

ft.  and  in. 

Area  in  feet. 

Diam.  in 
ft.  and  in. 

Circum.  in 
ft.  and  in. 

Area  in  feet. 

7    0 

21  Hi 

38-4846 

10    0 

31    5 

78-5400 

1 

22    3 

39-4060 

1 

31     8| 

79-8540 

2 

22    6J 

40-3388 

2 

31  Hi 

81-1795 

3 

22    94 

41-2825 

3 

32    2f 

82-5160 

4 

23    Of 

42-2367 

4 

32    5£ 

83-8627 

5 

23    2£ 

43-2022 

5 

32    8| 

85-'.?t> 

6 

23    6| 

44-1787 

6 

32  Hi 

86v.        ( 

7 

23  11 

45-1656 

7 

33    2| 

87-96J7 

8 

24     1J 

46-1638 

8 

33    6k 

89-3608 

9 

24    4£ 

47-1730 

9 

33    9i 

90-7627 

10 

24    7£ 

48-1926 

10 

34     0| 

92-1749 

11 

24  10| 

49-2236 

11 

34     3£ 

93-5986 

8    0 

25     1£ 

50-2656 

11    0 

34    6| 

95-0334 

1 

25    4f 

51-3178 

1 

34    9| 

964783 

2 

25     7i 

52-3816 

2 

35    0£ 

97-9347 

3 

25  11 

53-4562 

3 

35    4i 

99-4021 

4 

26    2fr 

54-5412 

4 

35    74 

100-8797 

5 

26    51 

55-6377 

5 

35  10| 

102-3689 

6 

26    8| 

567451 

6 

36     li 

103-8691 

7 

26  Hi 

57-8628 

7 

36    4£ 

105-3794 

8 

27    2| 

58-9920 

8 

36    7| 

106-9013 

9 

27    5| 

60-1321 

9 

36  lOf 

108-4342 

10 

27    9 

61-2826 

10 

37    2| 

109-9772 

11 

28    0£ 

62-4445 

11 

37    5| 

111-5319 

9    0 

28    3| 

63-6174 

12    0 

37    8| 

113-0976 

1 

28    6| 

64-8006 

1 

37  1H 

114-6732 

2 

28    94 

65-9951 

2 

38    2| 

116-2607 

3 

29    Oi 

67-2007 

3 

38    5| 

117-8590 

4 

29    31 

684166 

4 

38    8| 

119-4674 

5 

29    7 

69-6440 

5 

39    0 

121-0876 

6 

29  10* 

70-8823 

6 

39    34 

1227187 

7 

30     l^ 

72-1309 

7 

39    6| 

124-3598 

8 

30    4| 

73-3910 

8 

39    9| 

126-0127 

9 

30    7£ 

74-6620 

9 

40    Of 

127-6765 

10 

30  111 

75-9433 

10 

40     31 

129-ar>04 

11 

31     ll 

772362 

11 

40    61 

131  3360 

AREAS    Ol    CIRCLES. 


171 


Di:im.  in 
ft.  and  in. 

Circmn.  in 
ft.  and  in. 

Area  in  feet. 

Diam.  in 
ft.  and  in. 

Circum.  in 
ft.  and  in. 

Area  in  feet 

13  0 

40  10 

132-7326 

16  0 

50  3£ 

201-0624 

1 

41  li 

1344391 

1 

50  6^ 

203-1615 

2 

41  4| 

136-1574 

2 

50  9$ 

205-2726 

3 

41  71 

137-886? 

3 

51  0£ 

207-3946 

4 

41  10| 

139-6260 

4 

51  31 

209-5264 

5 

42  1| 

141-3771 

5 

51  64 

211-6703 

6 

42  41 

143-1391 

6 

51  10 

213-8251 

7 

42  8 

144-9111 

7 

52  U 

215-9896 

8 

42  11J 

146-6949 

8 

52  44 

218-1662 

9 

43  24 

148-4896 

9 

52  7| 

220-3537 

10 

43  54 

150-2943 

10 

52  10A 

222-5510 

11 

43  8| 

1521109 

11 

53  1| 

224-7603 

14  0 

43  111 

153-9384 

17  0 

53  41 

226-9806 

1 

44  2& 

155-7758 

1 

53  8 

229-2105 

2 

44  6 

157-6250 

2 

53  11J 

231  -4625 

3 

44  9$ 

159-4852 

3 

54  2i 

233-7055 

4 

45  04 

1613553 

4 

54  of 

235-9682 

5 

45  3£ 

163-2373 

5 

54  8£ 

2382430 

6 

45  6| 

1651303 

6 

54  11| 

240-5287 

7 

45  91 

167-0331 

7 

55  2$ 

242-8241 

8 

46  0$ 

168-9479 

8 

55  6 

2451316 

9 

46  4 

170-8735 

9 

55  9£ 

247-4500 

10 

46  7J 

172-8091 

10 

56  0| 

249-7781 

11 

46  Hi 

174-7565 

11 

56  3% 

2521184 

15  0 

47  1^ 

1767150 

18  0 

56  64 

2544696 

1 

47  4| 

1786832 

1 

56  91 

2568303 

2 

47  71 

180-6634 

2 

57  01 

2592033 

3 

47  10^ 

1826545 

3 

57  4 

2615872 

4 

48  24 

1846555 

4 

57  7\ 

263-9807 

5 

48  5i 

1866684 

5 

57  10.1 

2663864 

6 

48  8i 

1886023 

6 

58  1| 

268-8031 

7 

48  11| 

190-7260 

7 

58  44 

271-2293 

8 

49  2§ 

1927716 

8 

58  7j 

273-6678 

9 

49  51 

194-8282 

9 

58  10} 

2761171 

10 

49  8| 

1968946 

10 

59  2 

278-5761 

11 

50  0 

198-9730 

11 

59  5£ 

281-0472 

15* 


172    SQUARE   AND   CUBE    ROOTS    OF    NUMBERS. 


No. 

S.  R. 

C.  R. 

No.  I    S.  R. 

C.  R. 

No. 

S.  R.   l  C.  R. 

No. 

S.  R. 

C.  R. 

l 

1-0000 

1-0000 

55  |    7-4  161  |3-8029 

109 

10-4403!    -7768 

163 

12-7671 

5-4625 

2 

1-4142 

1-2599 

56 

7-4833  :  3-S'2JS 

111) 

10-4880 

•7914 

164 

12-8062 

5-4737 

3 

•7320 

1-4422 

57 

7-5498 

3-6485 

HI 

10-5356 

•8058 

166 

12-8452 

5-4848 

4 

2-0000 

1-5874 

to 

7-6157 

3  bTV- 

112 

10-5830 

•820:2 

i.6fl 

12-8840 

5-4958 

5 

2-2360 

1-7099 

59 

7-6811 

38929 

118 

10-6301 

•8345 

!67 

12-9228 

5-5068 

6 

2-4494 

1-8171 

60 

7  7459 

3-9i48 

114 

10-6770 

•84b8 

168 

12-9614 

5-5178 

7 

2-6457 

1-9129 

61 

7-8102 

3-9364 

115 

10-7238 

•8629 

169 

13-0000 

5-5287 

8 

2  -8284 

2-0000 

62 

7-8740 

3-9578 

116 

10-7703 

•876y 

170 

13-0384 

5-5396 

9 

30000 

2-0800 

u 

7-9372 

3-S7i,0 

111 

10-81S6 

•8909 

171 

13-0766 

5-5404 

10 

3-16-22 

2-1544 

64 

8-0000 

4-0000 

Us 

10-86-27 

•9048 

172 

13-1148 

5-5612 

11 

3-3166 

2-2239 

8-0622 

4-0207 

119 

10-9087 

•918-3 

173 

13-1529 

5-5720 

13 

3-  16n 

2-2894 

16 

8-1-240 

4-0412 

126 

10-9514 

•93v}4 

174 

13-1909 

5-53-27 

13 

J-6055 

2-3513 

67 

8-1853 

4-0515 

121 

11-0000 

•9460 

178 

13-2287 

5-5934 

14 

3-7413 

2-4101 

K 

8-2462 

4-0316 

122 

11-0453 

•9596 

i:.i 

13-2664 

5-50-10 

15 

3-87^9 

•2-4562 

99 

8-3066 

4-1015 

1-3 

11-0905 

•9731 

177 

13-3041 

5-6416 

16 

•0000 

•2-5198 

70 

83666 

4-1212 

124 

1  -1355 

•9866 

178 

13-3416 

5-6-252 

17 

•1231 

2-5712 

71 

8-4261 

4-1408 

125 

1   -1803 

0000 

171 

13-3790 

5-6357 

18 

"2426 

2-6207 

72 

84852 

4-1601 

126 

1   -2249 

5-0132 

(80 

13-4164 

5-6462 

19 

•3588 

2-6684 

73 

8-5440 

4-1793 

127 

1  -2694 

5-0265 

181 

13-4536 

5-6566 

20 

•4721 

2-7144 

7-1 

8-6023 

4-19a3 

1-2- 

1  -3137 

5-03S6 

183 

13-4907 

5-8670 

21 

•5825 

2*7589 

78 

8-6602 

4-2171 

129 

1   -3578 

5-0527 

183 

13-5-277 

5-6774 

22 

•6904 

2-8020 

7b 

8-7177 

4-2358 

130 

11-4017 

5-0657 

184 

13-5646 

5-6877 

23 

•7958 

2-8438 

77 

87749 

4-2543 

131 

1-4455 

5-0787 

186 

13-6014 

5-6980 

24 

•8939 

2-8844 

78 

8-8317 

4-2726 

132 

11-4891 

5-0916 

186 

13-6331 

5-7082 

25 

•0000 

2-9240 

79 

8-8881 

4-2908 

133 

1-5325 

5-1044 

181 

13-6747 

5-7184 

26 

5-0990 

2-9624 

w 

8-9442 

4-3088 

13! 

11-5758 

5-1172 

188 

13-7113 

5-7286 

27 

5-1961 

3-0000 

bi 

9-0000 

4-3267 

I3S 

1-6189 

5-1299 

!  8 

13-7477 

5-7387 

28 

5-2915 

3-0365 

b2 

9-0553 

4-3444 

!:;•> 

11-6619 

5-1425 

190 

13-7840 

5-74S8 

29 

53851 

3-0723 

S3 

9-1104 

4-3620 

137 

11-7046 

5-1551 

194 

13-8202 

5-7589 

30 

5-4772 

3-1072 

8! 

9-1651 

4-3795 

138 

11-7473 

5-1676 

192 

13-8564 

5-7689 

31 

55S77 

3-1413 

BS 

9-2195 

4-3968 

139 

11-7898 

5-1801 

193 

13-8924 

5-7789 

3-2 

565S3 

3-1748 

^ 

9-2736 

4-4UO 

140 

11-8321 

5-1924 

194 

13-9283 

5-7889 

33 

5-7445 

3-2075 

87 

9-3273 

4-4310 

I-il 

11-8743 

5-2048 

199 

13-9642 

5-7988 

34 

5-8309 

3-2396 

S3 

9-3808 

4-4479 

11,: 

11-9163 

5-2171 

196 

14-0000 

5-8087 

35 

5-9160 

3-2710 

BI 

9-4339 

4-4647 

149 

1-9582 

5-2293 

;  »7 

14-0a56 

5-8186 

36 

6-0000 

3-3019 

M 

9-4868 

4-4814 

144 

12-0000 

5-2414 

i  98 

14-0712 

5-8284 

37 

6-0827 

3-3322 

91 

9-5393 

4-4979 

I  -1-1 

12-0415 

5-2535 

198 

14-1067 

5*382 

38 

6  1644 

3-3619 

92 

9-5916 

4-5143 

146 

1-2-0830 

5-2656 

200 

14-1421 

5-8480 

39 

6-2449 

3-3912 

93 

9-6436 

4-5306 

147 

2-1243 

5-2776 

201 

14-1774 

5-8577 

40 

6-3245 

3-4199 

91 

9-6953 

4-5468 

148 

12-165~> 

5-2895 

202 

14-2126 

5-8674 

41 

6-4031 

3-4482 

05 

9-7467 

4-5629 

148 

12-2065 

5-3014 

303 

14-2478 

5-8771 

42 

6-4807 

3-4760 

B6 

9-7979 

4-5788 

150 

12-2474 

5-3132 

204 

14-2828 

5-8867 

43 

6-5574 

3-5033 

W 

9-8488 

4-5947 

151 

12-2882 

5-3250 

205 

14-3178 

5-8963 

44 

6  -6332 

3  5303 

98 

9-8994 

4-6104 

152 

2-3288 

5-336fr 

206 

14-3527 

5-S059 

45 

6-7r82 

3-55K8 

99 

9-9198 

4-6260 

153 

2-3693 

5-3484 

an 

14-3874 

5-9154 

46 

6-7823 

3-5830 

loo 

10-0000 

4-6415 

154 

2-4096 

5-360! 

208 

14-42-22 

5-9249 

47 

6-8556 

3-60M8 

!;,! 

10-0498 

4-6570 

155 

2-4498 

5-3716 

209 

14-4568 

5-9344 

48 

6-928-2 

3634-2 

ioa 

10-0995 

4-6723 

156 

2-4899 

5-3832 

210 

14-4913 

5-S439 

49 

7-0000 

3-6593 

103 

10-1488 

4-6375 

157 

2-5299 

5-3946 

21.1 

14-5258 

5-9533 

50 

70710 

3-6840 

104 

10-1980 

4-70'26 

158 

2-5698 

5-4061 

,-1-2 

14-5602 

5-9627 

51 

7  1414 

3-7084 

105 

10-2469 

4-7176 

159 

12-6095  '5-4175 

213 

14-5945 

5-9720 

52 

7-2111 

3-7325 

106 

10-2956 

4-7326 

160    12-6491  1  5-4288 

•21! 

14-6287   5-9814 

53 

7-2801 

3-7562 

107 

10-3440 

4-7474 

161    12-6885   5-4401 

•215 

1  4  -6628  !  5  -9907 

54 

7-3484 

3-7797 

108 

10-3923 

4-7622 

162    12-7279    5-4513 

216 

14-6969  6-0000 

To  find  the  gquare  or  cube  root  of  a  number  consisting  of  integers  and  decimate. 

Rule.  —  Multiply  the  difference  between  the  root  of  the  integer  part  of  the  jrjven 
number,  ami  the  root  of  the  next  higher  number,  by  the  decimal  part  of  the  give» 
number,  and  add  the  product  to  t!ie  root  of  the  given  integer  number;  the  sum  is  th« 
loot  required. 

Ex.   Required  the  square  root  of  20-321. 

Square  root  of  21  —  4-5825 
M        «     «  20=4-4721 

Di£      -  -1 104  X  -321+  4-4721  -4-507,  4c.,  the  root  required. 


VARNISHES,  173 


MISCELLANEOUS   NOTES 

VARNISHES. 

[From  Dr.  lire's  Dictionary  of  Arts  and  Manufactures.] 

White  Spirit  Varnish.  —  Sandarach,  250  parts ;  mas 
tie  in  tears,  64 ;  elemi  resin,  32 ;  Venice  turpentine, 
64;  alcohol  of  85  per  cent,  1000  parts  by  measure 
The  turpentine  is  to  be  added  after  the  resins  are  dis- 
solved. This  is  a  brilliant  varnish,  but  not  so  hard  as 
to  bear  polishing. 

Varnish  for  the  Wood  Toys  of  Spa. — Tender  copal, 
75  parts ;  mastic,  12-5 ;  Venice  turpentine,  6*5 ;  alcohol 
of  95  per  cent.,  100  parts  by  measure ;  water,  ounces  — 
for  example,  if  the  other  be  taken  in  ounces.  The 
alcohol  must  be  first  made  to  act  upon  the  copal,  with 
the  aid  of  a  little  oil  of  lavender  or  camphor,  if  thought 
fit;  and,  the  solution  being  passed  through  a  linen 
cloth,  the  mastic  must  be  introduced.  After  it  & 
dissolved,  the  Venice  turpentine,  previously  melted  in 
a  water  bafh,  should  be  added.  The  lower  the  tem- 
perature at  which  these  operations  are  carried  on,  the 
more  beautiful  will  the  varnish  be.  This  varnish  ought 
to  be  very  white,  very  drying,  and  capable  of  being 
smoothed  with  pumice-stone  and  polished. 

Varnish  for  Cabinet-Makers.  —  Pale  shellac,  750 
parts ;  mastic,  64 ;  alcohol  of  90  per  cent.,  1000  parts 
by  measure.  The  solution  is  made  in  the  cold,  with 
the  aid  of  frequent  stirring.  It  is  always  muddy,  and 
is  employed  without  being  filtered.  With  the  same 
resins  and  proof  spirit,  a  varnish  is  made  for  the  book- 
binders, to  do  over  their  morocco  leather. 

Crystal  Varnish.  —  Procure  a  bottle  of  Canada  bal- 
eam,  which  can  be  had  at  any  druggist's ;  draw  out  the 
cork  and  set  the  bottle  of  balsam  at  a  little  distance 


174  MISCELLANEOUS    NOTES. 

from  the  fire,  turning  it  round  several  times,  until  tho 
heat  has  thinned  it ;  then  have  something  that  wil} 
hold  as  much  as  double  the  quantity  of  balsam ;  carry 
the  balsam  from  the  fire,  and,  while  fluid,  mix  it  with 
the  same  quantity  of  good  turpentine,  and  shake  them 
together  until  they  are  well  incorporated.  In  a  few 
days,  the  varnish  is  fit  for  use;  particularly  if  it  is 
poured  into  a  half-gallon  glass  or  stone  bottle,  and  kept 
in  a  gentle  warmth.  This  varnish  is  used  for  maps, 
prints,  charts,  drawings,  paper  ornaments,  &c. 

The,  Chinese  Varnish  is  obtained  from  a  tree  which 
grows  in  Cochin-China,  China,  and  Siam.  It  forms 
the  best  of  all  varnishes. 

Gold  Lacker.  —  Put  into  a  clean  four-gallon  tin  1  Ib. 
ground  turmeric,  1£  oz.  powdered  gamboge,  3£  Ibs. 
powdered  gurn  sandarach,  f  Ib.  snellac,  and  2  galls, 
spirits  of  wine.  Afler  being  dissolved  and  strained, 
add  1  pint  of  turpentine  varnish,  well  mixed. 

Red  Spirit  Lacker.  —  2  galls,  spirits  of  wine;  1  Ib. 
dragon's-blood;  3  Ibs.  Spanish  annotto;  3£  Ibs.  gum 
sandarach ;  2  pints  turpentine ;  —  made  exactly  as  the 
gold  lacker. 

The  Famish  of  Watin,  for  Gilded  Articles.  —  Gum 
la*  in  grain,  125  parts ;  gamboge,  125 ;  dragon's-blood, 
125;  annotto,  125;  saffron,  32.  Each  resin  must  be 
dissolved  in  1000  parts  by  measure  of  alcohol  of  90 
per  cent.  Two  separate  tinctures  must  be  made  with 
the  dragon's-blood  and  annotto,  in  1000  parts  of  such 
alcohol ;  and  a  proper  proportion  of  each  should  be 
added  to  the  varnish,  according  to  the  shade  of  golden 
color  wanted. 

Transfer  Varnish.  —  For  fixing  engravings  or  litho- 
graphs upon  wood,  a  varnish  called  mordant  is  used  in 
France,  which  differs  from  others  chiefly  in  containing 
more  Venice  turpentine,  to  make  it  sticky.  1.  consists 
of  sandarach,  2~>0  parts;  mastic  in  tears,  64;  rosin, 
125;  Venice  turpentine,  250;  alcohol,  1000  parts  b) 
measure. 

Common  Mastic  Varnish.  —  Put  as  much  gum  mastic, 


VARNISHES.  175 

unpicked,  into  the  gum-pot,  as  may  be  required;  and 
to  every  2|  Ibs.  of  gum,  pour  in  1  gall,  of  cold  turpen- 
tine ;  set  the  pot  over  a  very  moderate  fire,  and  stir  it 
Be  careful,  when  the  steam  of  the  turpentine  rises  near 
the  mouth  of  the  pot,  to  cover  with  a  piece  of  woollen 
cloth,  and  carry  it  out  of  doors,  as  the  vapor  is  very  ap< 
to  catch  fire.  A  few  minutes'  low  heat  will  perfectly 
dissolve  8  Ibs.  of  gum,  which  will,  with  4  galls,  of 
turpentine,  produce,  when  strained,  4^  galls,  of  varnish; 
to  which  add,  while  yet  hot,  5  pints  of  pale  turpentine 
varnish,  which  improves  the  body  and  hardness  of  the 
mastic  varnish. 

Pale  Brass  Lacker.  —  2  galls,  spirits  of  wine ;  3  oz. 
Cape  aloes ;  cut  small  1  Ib.  fine  pale  shellac ;  1  oz. 
gamboge,  cut  small ;  no  turpentine  ;  —  varnish  made 
exactly  as  before.  But  observe,  that  those  who  make 
lackers  frequently  want  some  paler  and  some  darker; 
and  sometimes  inclining  more  to  the  particular  tint  of 
certain  of  the  component  ingredients.  Therefore,  if  a 
4  oz.  phial  of  a  strong  solution  of  each  ingredient  be 
prepared,  a  lacker  of  any  tint  can  be  produced  at  any 
time. 

Iron-Work  Black.  —  Put  48  Ibs.  asphaltum  into  an 
iron  pot,  and  boil  for  4  hours  ;  during  the  first  2  hours, 
introduce  7  Ibs.  litharge,  3  Ibs.  dried  copperas,  and  10 
galls,  boiled ;  add  1-eighth  Ib.  run  of  dark  gum,  with 
2  galls,  hot  oil.  A  tier  pouring  the  oil  and  gum,  con- 
tinue the  boiling  2  hours,  or  until  it  will  roll  into  hard 
pills,  like  Japan.  When  cool,  thin  it  off  with  30  galls. 
turpentine,  or  until  it  is  of  proper  consistence.  This 
varnish  is  intended  for  the  iron- work  of  coaches  and 
other  carriages,  &c. 

To  make  Cloth,  Silk,  fyc.  water-proof.  —  Mix  equal 
quantities  of  alum  and  acetate  of  lead,  and  dissolve 
the  mixture  in  a  gallon  and  a  half  of  boiling  water 
When  the  solution  has  cooled,  remove  the  supernatant 
liquid  from  the  sediment,  which  consists  of  sulphate  of 
lead,  and  it  is  ready  for  use.  Any  article  of  dress, 
wnen  well  saturated  in  this  liquid,  and  allowed  to  dry 


176  SOLDERS. 

slowly,  bears  the  action  of  boiling  water,  and  does  not 
permit  it  to  pass  through,  although  steam  and  air  pene- 
trate it  freely. 

Cement  for  China,  Glass,  tyc.  —  To  1  oz.  gum  mastic 
add  as  much  spirits  of  wine  as  will  dissolve  it ;  soak 
1  oz.  isinglass  in  water  till  it  is  quite  soft,  then  dis- 
solve it  in  pure  brandy  till  of  the  consistence  of  glue  ; 
to  this  add  |  oz.  gum  ammoniac,  well  rubbed  and 
mixed.  Put  now  the  two  mixtures  together  in  a  vessel 
over  a  gentle  heat,  till  properly  united,  and  the  cemen' 
is  ready  for  use.  It  must  be  kept  in  a  phial  wel 
stopped ;  and,  when  about  to  be  used,  it  ought  to  bi 
set  in  boiling  water  to  soften. 

Preparation  for  Silver  Solution.  —  Take  1  pint  of 
pure  rain  or  distilled  water;  add  to  it  2  oz.  cyanide  oi 
potassium  ;  shake  them  together  occasionally,  until  the 
hitter  is  entirely  dissolved,  and  allow  the  liquid  to 
become  clear ;  then  add  4  oz.  oxide  of  silver,  which 
will  very  speedily  dissolve ;  and,  after  a  short  time,  8 
clear,  transparent  solution  will  be  obtained. 

Preparation  of  Gold  Solution.  —  Warm  a  pint  of 
pure  rain  water,  and  dissolve  in  it  2  oz.  cyanide  of 
potassium ;  then  add  |  oz.  oxide  of  gold ;  the  solution 
will  at  first  be  yellowish,  but  will  soon  subside  to  white 


SOLDERS. 

For  Lend.  —  Melt  1  part  of  block  tin,  and,  when  in 
a  state  of  fusion,  add  2  parts  of  lead.  Resin  should  be 
used  with  this  solder. 

For  Tin.  —  Pewter,  4  parts ;  tin,  1 ;  bismuth,  1 ;  melt 
them  together.  Resin  is  also  used  with  this  solder. 

For  Iron.  —  Tough  brass,  witn  a  small  quantity  of 
borax. 


SCREWS. 


177 


CAPACITY    OF    CISTERNS    IN    GALLONS. 


For  each  10  Inches  in  Depth. 


2  feet  diameter, 
2A  "  « 

3  "  " 
3£  "  " 

4  i{  ll 

44  "  " 

b~  "  u 


?: 

74    « 


19-5 

8    feet  diameter.  .         313-33 

30-6 

8£    « 

353-72 

4-1-06 

9     " 

u 

396-56 

59-97 

9A    " 

it 

461-40 

78-33 

10     « 

u 

489-2C 

99-14 

11      « 

tt 

592-4C 

122-40 

12     " 

ii 

705- 

148-10 

13     « 

tt 

827-4 

176-25 

14     « 

it 

959-6 

206-85 

15     « 

tt 

1101-6 

'239-88 

20     « 

tt 

1958-4 

275-40 

25     " 

u 

3059-9 

SCREWS. 

Table  showing  the  Number  of  Threads  to  an  Inch  in 
V -thread  Screws. 


Diam.  in  inches,  .  .  *  lV  t  iVf  I  I    I  *    1* 

No.  of  threads,    .  .  20    18    16    14   12  11  10  9   8     7 


*i 

7 


Diam.  in  inches,  .  .  1£ 
No.  of  threads,     .  .  6 


5     5     4^ 


4     4 


2|    3 


3^   3£    34 


Diam.  in  inches,  .  .  3|     4 
No.  of  threads,    .  .  3      3 


4|      5 

2^     2| 


5|     6 


The  depth  of  the  threads  should  be  half  their  pitch. 
The  diameter  of  a  screw,  to  work  in  the  teeth  of  a 
wheel,  should  be  such,  that  the  angle  of  the  threads 
does  not  exceed  10°. 


178 


WEIGHTS    OF    VARIOUS    SUBSTANCES. 


RECAPITULATION    OF    WEIGHTS    OF    VARIOUS 
SUBSTANCES. 


Names. 

Cubic  foot  in  Ibs. 

Cubic  inch  in  Ibs 

Cast  iron       .     .     . 
Wrought  iron  .     . 
Steel   

450-55 

486-65 
489-8 

•26*07 
•2816 
•2834 

Copper     .... 
Lead   
Brass  .     .     .     .     . 

555- 

708-75 
5I57-75 

•32118 
•41015 
•3112 

Tin     

456- 

•263 

White  pine  .     .     . 
Salt  water  (sea)     . 
Fresh  water     .     . 
Air     

29-56 

64-3 
62-5 
•07529 

•0171 
•03721 
•03616 

Steam      .... 

•03689 

— 

CAST  IRON  expands  -i^Vinj-  of  its  length  for  one 
degree  of  heat ;  greatest  change  in  the  shade,  in  this 
climate,  YTTZT  °f  *ts  length ;  exposed  to  the  sun's  rays, 
BTUI?T<T  ?  shrinks  in  cooling  from  ^  to  ^F  of  its  length ; 
is  crushed  by  a  force  of  93,000  Ibs.  upon  a  square  inch; 
will  bear,  without  permanent  alteration,  15,300  Ibs.  upon 
a  square  inch,  and  an  extension  of  J^ITIT  of  its  length. 
Weight  of  modulus  of  elasticity  for  a  base  of  an  inch 
square,  18,400,000  Ibs.;  height  of  modulus  of  elasticity, 
5,750,000  feet 

WROUGHT  IRON  expands  TTuWu  °f  ^ts  length  for 
one  degree  of  heat;  will  bear,  on  a  square  inch,  with- 
out permanent  alteration,  17,800  Ibs.,  and  an  extension 
in  length  of  -^Wi  cohesive  force  is  diminished  -guVij 
by  an  increase  of  one  degree  of  heat.  Weight  of 
modulus  of  elasticity  for  a  base  of  an  inch  square, 
24,920,000  Ibs.  ;  height  of  modulus  of  elasticity 
7,550,000  feet. 


PART     SECOND. 


INTRODUCTION. 


CHOICE   OF  A  PROFESSION:    RESPECT ABI 
LITY  OF  MECHANICAL  TRADES. 

THE  choice  of  a  pursuit  in  life,  one  of  the 
most  important  practical  questions  upon  which 
a  young  person  is  ever  called  to  decide,  is  often 
determined  by  the  most  trifling  circumstances, 
and  without  the  slightest  aid  from  judgment  or 
reflection.  One  youth  becomes  a  soldier  be- 
cause his  great  grandfather  was  at  the  taking 
of  Cape  Breton,  or  his  great  uncle  signalized 
himself  in  Braddockns  fight;  another  studies 
medicine,  and  hopes  to  be  almost  an  infallible 
doctor,  because  he  is  the  seventh  son  of  a 
seventh  son ;  while  a  third  chooses  the  profes- 
sion of  the  law  for  no  better  reason  than  that 
his  sponsors  at  the  baptismal  font,  chose  to 
call  him  William  Wirt,  or  Daniel  Webster,  or 
John  Sergeant.  Surely  this  is  not  that  practi- 
cal wisdom  which  adapts  the  fittest  means  to 
the  noblest  ends  The  choice  of  a  profession 
16 


IQQ  INTRODUCTION. 

in  life  is  at  least  worthy  of  such  a  considera- 
tion as  common  sense  would  dictate  in  any 
other  case,  where  success  in  an  enterprise  ds- 
prticls  upon  fitness  for  undertaking  it.  Men  do 
not  expect  to  gather  grapes  from  thorns,  nor 
figs  from  thistles;  yet  they  expect  their  sons 
and  daughters  to  succeed  ii>  pursuits  for  which 
they  are  wholly  .incapacitated  by  talents,  dispo- 
sition or  education  ;  and  what  is  still  more  un- 
reasonable, they  expect  them  to  be  happy  in 
situations  which  are  totally  uncongenial  to  their 
nature. 

One  reason  why  parents  and  guardians  fall 
so  frequently  into  errors  on  this  point, — errors, 
too,  which  they  lead  those  under  their  charge 
to  embrace, — is  the  vain  imagination  that  there  is 
a  great  and  essential  difference  in  the  respecta 
bility  of  those  pursuits  which  are  generally 
admitted  to  be  honest.  The  respectability  of  a 
profession,  I  suppose  it  will  be  admitted,  must 
depend  in  a  great  measure  on  the  respectable 
character  of  its  members,  taken  collectively,  or 
regarded  with  reference  to  the  most  brilliant 
examples.  If  we  adopt  this  standard,  it  will  be 
found  no  easy  matter  to  establish  a  claim  to 
superior  respectability  in  favour  of  any  one 


COMPARISON  OF  PROFESSIONS.  Jg] 

trade,  or  profession,  or  of  any  class  of  trades 
or  professions,  j 

If  it  should  be  asserted  that  the  learned  pro- 
fessions of  law,  physic  and  divinity  are  more 
respectable  than  the  pursuits  of  commerce,  me- 
chanics or  agriculture,  it  might  be  easily  shown 
that  taken  collectively,  the  members  of  these 
latter  professions  or  trades  possess  more  wealth, 
ease  and  independence  than  those  of  the  learn- 
ed ones ;  and  moreover,  that  among  them  as 
brilliant  examples  of  mental  pre-eminence,  pa- 
triotism and  public  spirit  may  be  pointed  out 
as  among  those  of  the  more  learned  professions 

In  fact,  in  a  country  like  ours,  such  a  claim 
of  superior  respectability  on  behalf  of  any  pro- 
fession is  preposterous ;  and  yet  it  is  constantly 
assigied  by  purse-proud  fathers  and  silly 
mothers  &»  a  reason  for  determining  their  chil- 
dren's pursuits  in  life.  There  is  a  very  general 
impression  tnat  a  merchant,  a  clergyman,  doc- 
tor or  lawyer  stands  higher,  and  should  stand 
higher,  in  the  social  scale  than  a  mechanic  or 
tanner.  But  such  is  not  the  fact,  as  a  general 
principle;  or,  which  results  in  the  same  thing, 
it  in  a  particular  instance,  a  particular  merchant, 
for  example,  stands  higher  in  social  estimation 
man  a  particular  mechanic,  it  is  not  on  accoun-* 


182  INTRODUCTION. 

of  the  respective  means  by  which  they  earn 
then  livelihood.,  but  because  the  merchant  in 
this  instance  has  claims  by  wealth,  family  in- 
fluence or  education,  which  the  mechanic  has 
no! ;  ami  by  passing  into  the  next  street,  and 
taking  another  example,  you  will  find  the  tables 
completely  turned,  and  the  mechanic  in  the 
enjoyment  of  a  social  position  to  which  the 
merchant  cannot  aspire.  This  fact  is  sufficient 
to  prove  that  a  man  of  one  trade  or  profession 
does  not  take  a  lower  position  in  society  than 
another  of  a  different  profession,  simply  on 
account  of  the  di  fie  rent  modes  by  which  they 
subsist,  but  by  reason  of  other  circumstances 
which  are  wholly  independent  of  this  conside- 
ration. Mr.  A.,  who  is  a  merchant,  does  not, 
for  example,  decline  an  intimate  acquaintance 
and  social  intercourse  with  Mr.  B.,  because  Mr. 
B.  is  a  mechanic,  but  because  their  favourite 
topics  of  conversation,  their  tastes  and  pursuits, 
are  different;  and  this  is  clearly  apparent  from 
another  fact,  viz. : — that  whenever  two  persons 
of  totally  different  professions  happen  to  meet 
frequently  upon  some  common  ground  of 
science  or  the  fine  arts,  in  their  leisure  hours 
they  immediately  recognise  each  other's  natu- 
ral equality  and  become  familiar  companions 


RESPECTABILITY  OF  TRADES.  Jg3 

They  collect  plants,  or  minerals,  or  perform 
chemical  or  philosophical  experiments  together; 
they  unite  in  the  same  pursuits  during  their 
leisure  hours,  and  become  daily  moie  and  more 
assimilated  in  mind  and  character,  as  well  as 
in  their  favourite  recreations,  until  they  are 
hound  together  by  the  strictest  bonds  of  friend- 
ship. There  is,  therefore,  no  necessary  or  es- 
sential difference  in  the  respectability  of  differ- 
ent trades  and  professions;  and  there  is  no 
social  estrangement  between  their  members, 
which  may  not  be  overcome  by  precisely  the 
same  means  which  constitute  the  cause  of  inti- 
macy in  other  circumstances.  In  our  country, 
therefore,  in  point  of  real  and  essential  respect- 
ability, all  trades  and  professions  are  equal ;  and 
the  social  position  which  a  man  enjoys,  and 
the  degree  of  respect  which  he  is  able  to  com- 
mand, depend  not  upon  his  trade,  but  upon 
his  individual  character.  4 

If,  in  every  part  of  the  United  States,  the 
stupid  prejudice  which  would  exclude  the  me- 
chanic or  the  farmer  from  any  society  to  which 
his  intelligence  and  good  manners  -  entitle  him, 
is  not  thoroughly  exploded,  the  time  has  cer- 
tainly arrived  when  it  is  no  longer  to  be  avowed 
bv  well  bred  people.  In  fact,  the  rule  which 


1§4  INTRODUCTION. 

would  exclude  a  man  from  any  drawing-room 
in  the  land,  on  the  simple  ground  of  his  being 
a  mechanic',  would  have  excluded  from  the 
same  drawing-room  such  men  as  Nathaniel 
Bowditch,  who  was  a  mariner  by  trade ;  Roger 
Sherman,  who  was  a  shoemaker  by  trade  ;  Ben- 
jamin Franklin,  late  ambassador  to  the  Court 
of  Versailles,  who  was  a  printer  by  trade ;  and 
George  Washington,  a  very  respectable  man  of 
the  last  century,  who  was  a  surveyor  by  trade, 
But  the  imaginary  respectability  which  a  man 
may  happen  to  enjoy  from  his  position  in  so- 
ciety, is  not  by  any  means  the  first  and  most 
mip^rtant  thing  to  be  considered  in  the  choice 
of  a  profession.  It  should  not  be  the  leading 
motive  in  determining  the  choice  of  the  parent ; 
neither  should  it  be  the  main  consideration  in 
the  mind  of  the  young  person  himself.  There 
is  another,  and  a  much  more  important  poin<- 
which  claims  and  should  receive  the  prece- 
dence. Every  parent  in  making  choice  of  a 
profession  for  his  son,  and  every  son  in  making 
the  same  choice  for  himself,  should  seriously 
and  deliberately  inquire,  what  profession  affords 
the  best  chance  for  happiness  ; — happiness,  in 
il«e  noblest  and  broadest  sense — happiness 
which  consists  in  contentment,  independence 


RESPECTABILITY  OF  TRADES.  Jg/J 

and  real  usefulness — happiness,  which  begins 
in  the  conscientious  and  successful  discharge 
of  duty  on  earth,  and  reaches  forward  to  the 
unerring  retribution  of  a  future  world. 

The  inquiry  which  is  thus  presented  is  a 
very  extensive  one.  It  admits  of  whole  years 
of  investigation — whole  volumes  of  disquisi- 
tion to  treat  it  at  large,  and  apply  it  to  any 
considerable  portion  of  the  cases  that  might 
arise.  In  order,  therefore,  to  avoid  running 
into  useless  generalities,  I  shall  devote  the  short 
space  which  is  allotted  to  me  on  the  present 
occasion,  to  a  very  small  part  of  this  great  sub- 
ject, and  shall  consider  that  part  in  a  single 
point  of  view.  I  propose,  in  the  outset  of  the 
present  work,  to  inquire  what  opportunities  are 
afforded  for  usefulness,  happiness,  and  real  re- 
spectability by  the  mechanical  trades — in  other 
words,  to  inquire  how  a  mechanic  may  be  use- 
ful, happy  and  respectable.  In  the  succeeding 
chapter  I  shall  consider  the  first  branch  of  the 
subject. 


THE  YOUNG  MECHANIC 


CHAPTER  L 

THE   MECHANIC  SHOULD  BE   MASTER  OF 
HIS  TRADE. 

IN  order  to  become  useful,  respectable,  and 
nappy,  it  appears  to  me  to  be  necessary,  IN  THE 
FIRST  PLACE,  that  the  mechanic  should  be- 
come a  thorough  master  of  his  trade.  Having 
made  a  deliberate  choice  of  that  pursuit,  by 
which  he  is  to  gain  his  livelihood,  it  is  a  mat- 
ter of  the  utmost  importance  that  he  should 
devote  the  energies  of  his  mind  to  the  business 
unreservedly,  until  he  has  mastered  all  its  prin- 
ciples and  details.  It  is  by  this  means  only 
that  hft  can  use  it  with  ease  and  satisfaction  as 
the  instrument  of  success  in  the  world.  The 
incapable,  or  half  taught  mechanic,  always 
works  at  a  ruinous  disadvantage.  He  can 
neither  command  the  highest  prices  for  the  pro- 
ducts of  his  art,  nor  superintend  with  intelli- 
gence and  authority  the  workmen  under  his 
care.  He  is  in  constant  danger  of  failure  in  his 
business,  or  of  abandoning  it,  through  sheer 
disgust,  only  to  take  up  some  other  pursuit  for 
which  he  is  totally  unfitted  by  education.  It 


APPRENTICESHIP.  Jg^ 

is  a  laudable  ambition,  therefore,  which  makes 
him  aspire  to  be  first  among  his  fellows.  Jlut 
Ccesar  aid  nullus — a  master  mechanic,  or  no 
mechanic  at  all — should  be  his  motto. 

1.  In   order  to  render  himself  a  thorough 
proficient  in   his   trade,  the  mechanic   should 
serve  out  his  complete  apprenticeship.     Justice 
to  himself,  as  well  as  to  his  master,  dictates  this 
course.     Nor  is  it  less  a  matter  of  policy  than 
of  moral  duty.     Even  if  he  should  deem  him- 
self capable  of  undertaking  the  management  of 
business  for  himself  before  he  has  half  com- 
pleted his  apprenticeship,  it  is  a  much  safer  and 
wiser  course  to  remain  in  a  subordinate  capa- 
city till  he  has  attained  the  age  of  manhood, 
than  to  rush  upon  the  heavy  duties  an^l  icarful 
responsibilities  of  active  life  before  his  judg- 
ment is   matured,   his   understanding   ripened, 
and  his  nerves  hardened  for  the  rough  encoun- 
ter of  conflicting  interests  and  unforeseen  emer- 
gencies. 

2.  At  the  same  time  that  I  counsel  the  ap- 
prentice to  serve  out  his  whole  time,  I  would 
strenuously  urge  upon  him  the  importance  of 
devoting  any  leisure  moments  that  he  may  have 
at  his  command,  each  day,  to  the  cultivation  of 
his  mind.     The  parent  or  guardian,  in  becoming 


188  THE  YOUNG  MECHANIC. 

a  party  to  indentures,  should  be  careful  to  ha\e 
a  clause  inserted  by  which  a  certain  portion  of 
time  shall  be  secured  to  the  apprentice  for  men- 
tal cultivation ,  and  when  this  i&  done  the  ap- 
prentice should  regularly  conseci  ite  this  time' 
to  its  legitimate  purpose.  In  our  large  cities 
facilities  for  this  purpose  are  judiciously  afford- 
ed by  the  beneficent  provisions  of  Mechanics' 
Institutes, Lyceums  and  Libraries;  but  even  in 
situations  where  such  opportunities  are  not  af- 
forded, we  know  by  many  illustrious  examples 
that  knowledge  may  be  pursued  and  attained 
under  the  most  discouraging  difficulties.  Where 
that  good  seed,  the  love  of  science,  has  been 
once  implanted,  it  will  spring  up  and  grow  and 
flourish,  though  pelted  by  storms  of  adversity, 
and  chilled  by  the  coldness  of  neglect.  It  is 
this  consideration  which  encourages  the  teacher 
who  has  the  future  apprentice  under  his  care, 
to  instil  into  his  opening  mind  the  most  liberal 
and  exalted  views  of  the  real  beauty,  as  well  as 
utility,  of  science  and  literature. 

But  why,  it  may  be  inquired,  should  the  me- 
chanic be  inspired  with  the  love  of  science  and 
literature  ?  I  answer,  that  the  mechanic  should 
learn  to  love  these  intellectual  pursuits  for  two 


MENTAL  CULTIVATION.  Jgg 

reasons : — First,  because  he  is  a  mechanic;  and 
secondly,  because  he  is  a  man. 

If  the  physician,  the  lawyer,  the  statesman, 
and  the  divine  avail  themselves  of  the  assist- 
ance of  science  and  literature  in  their  several 
professions,  the  mechanic  has  still  stronger  in- 
ducements for  doing  the  same  thing ;  for  to 
none  of  these  professions  are  the  results  of 
science  so  directly  applicable,  and  for  none  of 
them  are  the  recreations  of  literature  so  appro- 
priate or  gratifying.  By  making  himself  mas- 
ter of  those  principles  of  science  which  are 
most  intimately  connected  with  his  trade,  the 
mechanic,  while  he  is  satisfying  a  liberal  cu- 
riosity, may  possibly  be  approaching  some 
brilliant  discovery,  which  will  speedily  conduct 
him  to  fortune  and  fame;  and  if  the  lighter 
reading,  generally  termed  literature,  promises 
no  such  result,  it  affords  him  the  most  dignified 
and  innocent  means  of  amusement,  and  pre- 
serves the  vigour  and  increases  the  brightness 
of  his  intellect.  He  should,  therefore,  learn  to 
appreciate  such  pursuits,  because  they  are  fitting 
and  proper  to  him  as  a  mechanic. 

He  may  also  claim  them  as  his  own,  upon 
the  broad  principle,  that  wherever  there  is  a 
human  intellect  to  be  cultivated,  there  is  a  na- 


]90  THE  YOUNG  MECHANIC 

tural  and  indefeasible  right  to  the  brightest  de* 
gree  of  cultivation  which  it  can  attain. 

I  remark,  in  the  next  place,  that  the  mechanic, 
in  order  to  render  himself  a  complete  mastei 
of  his  trade,  should  possess  himself  of  new 
discoveries  in  science  which  are  applicable  to 
his  purposes,  and  should  actually  apply  them 
to  the  improvement  of  his  trade. 

There  never  was  a  time  since  Lord  Bacon 
first  placed  in  the  hands  of  philosophy  the 
right  instrument  of  investigation,  when  men  of 
science  were  more  actively  and  successfully 
engaged  in  developing  the  materials  and  pro- 
cesses directly  applicable  to  the  advancement 
of  the  mechanic  arts,  than  the  present.  The 
forest  and  the  mountain,  the  mine  and  the  river, 
the  deep  bosom  of  the  ocean  itself — all  are 
literally  ransacked  by  the  ardent  devotees  of 
science,  in  pursuit  of  new  substances  which 
may  minister  to  the  sustenance  or  pleasure  of 
man,  or  may  open  to  the  gaze  of  liberal  cu- 
riosity the  wonders  of  creative  power.  The 
Fcientific  traveller  brings  home  the  products  of 
vlistant  lands  to  be  naturalized  in  his  own  coun- 
try, and  thus  supply  new  materials  for  the  use- 
ful arts ;  the  mechanical  philosopher  is  con- 
stantly adding  to  the  number  of  known  motive 


USE  OF  LEISURE  TIME.  jgj 

powers ;  the  chemist  is  discovering  new  sub- 
stances, and  making  new  developements  and 
combinations  of  the  powers  of  those  already 
known ;  while  the  press,  by  means  of  the  ai  t 
preservative  of  all  arts,  is  bringing  the  icsult 
of  all  these  labours  and  inquiries  u  home  to  the 
bosoms  and  business  of  men."" 

At  such  a  time  it  becomes  not  the  mechanic 
to  be  an  idle  or  regardless  spectator  of  all  this 
activity.  In  the  leisure  moments  which,  by  an 
ordinary  arrangement  of  his  labours,  every  man 
may  redeem,  he  should  direct  his  attention  to 
the  progress  of  discovery  in  chemistry,  me- 
chanical philosophy  and  natural  history,  which 
have  a  direct  bearing  on  his  trade.  He  should 
attach  himself  to  that  mechanics'  institute  or 
lyceum  which  affords  him  the  best  means  of 
improvement  by  its  lectures,  experiments,  and 
library.  He  should  cultivate  the  acquaintance 
of  those  scientific  men  who  have  the  good 
sense  to  appreciate  the  society  of  intelligent 
practical  mechanics,  and  he  should  apply  the 
results  of  his  inquiries,  so  far  as  it  may  be  ju- 
diciously done,  to  the  perfecting  of  his  own 
manufactures.  In  recommending  such  a  course 
to  the  young  mechanic,  I  know  that  1  am  no< 
urging  upon  him  vain  speculations  in  visionary 
17 


192  THE  YOUNG  MECHANIC. 

schema.  That  such  a  course  is  precisely  the 
one  best  calculated  to  improve  and  develope 
the  mechanical  arts,  is  clearly  apparent  when- 
ever an  exhibition  of  the  products  of  American 
industry  is  opened  by  any  one  of  the  societies 
constituted  and  supported  by  mechanics  for 
this  very  purpose.  A  single  exhibition  of  the 
Franklin  Institute  establishes  with  .more  cer- 
tainty tfian  a  whole  volume  of  arguments,  the 
soundness  of  that  policy  which  leads  the  me- 
chanic to  devote  his  winter  evenings  to  scientific 
pursuits,  and  to  apply  the  result  of  his  study 
to  the  improvement  of  his  own  trade. 


ADHERENCE  TO  TRADE. 


CHAPTER  II. 

THE  MECHANIC  SHOULD  REMAIN  AT 
TACHED  TO  HIS  TRADE. 

THIS  is  not  all  that  is  requisite  for  the  use- 
fulness, happiness,  and  respectability  of  the 
mechanic.  In  order  to  secure  these  objects  fully, 
I  maintain,  in  the  second  place,  that  it  is  neces- 
sary for  him  to  remain  attached  to  his  trade. 
Recent  events  in  this  country  have,  I  think, 
sufficiently  demonstrated  the  pernicious  ten- 
dency of  that  ambitious  restlessness  which  has 
lately  pervaded  all  classes  of  people,  and  made 
almost  every  man  regard  his  business  whatever 
it  happened  to  be,  as  merely  the  stepping  stone 
to  something  apparently  higher.  Apparently, 
I  say,  for  we  have  seen  in  many  instances  that 
mechanics,  who  were  slowly  and  surely  ac- 
quiring the  means  of  independence  and  com- 
fort, have  dashed  into  wild  speculations,  in 
hopes  to  rise  to  some  imaginary  height  of 
wealth  and  importance ;  but  when  the  glittering 
bauble  was  almost  within  their  reach,  have 
found  it  suddenly  eiude  their  grasp  and  leave 


194  TTIE  YOUNG  MECHANIC. 

them  to  regret  the  loss  of  all  which  they  had 
been  toiling  for  years  to  acquire. 

Contentment,  like  every  other  Christian  duty, 
has  a  great  many  excellent  uses.  Jt  is  good 
for  the  mind,  for  the  body,  and  for  the  estate 
of  every  man.  It  tranquillizes  the  spirit,  it  pre- 
serves the  health,  and  it  promotes  that  steady 
economy  which  leads  to  competency ;  often  to 
affluence.  The  man  who  is  satisfied  with  the 
position  which  Providence  has  assigned  him, 
and  endeavours  to  make  himself  useful  in  that 
position,  presents  a  vastly  more  respectable 
figure  than  one  who  is  constantly  struggling  to 
place  himself  in  a  different  position.  The  fruits 
of  this  struggle  are  harassing  cares,  jealous 
heart-burnings,  hazardous  enterprises,  and  often 
debt  and  ruin.  There  is  an  old  and  homely 
saying,  applicable  to  every  one  who  has  been 
brought  up  to  a  regular  trade  or  profession — a 
saying  full  of  practical  wisdom,  which  many 
have  hitherto  disregarded,  but  which  will  be 
better  observed  in  years  to  come — u  Keep  your 
shop,  and  your  shop  will  keep  you."  This 
saying,  as  I  have  already  intimated,  is  a  whole- 
some one  for  any  man  who  labours  for  his 
subsistence,  whether  it  be  with  his  head  or  hia 


KEEP  YOUR  SHOP.  JQ^ 

hands;  but  for  the  mechanic  it  is  the  ark  of 
safety. 

In  some  foreign  countries  it  is  the  custom  for 
mechanics  to  form  associations,  of  which  one 
of  the  leading  objects  is  to  retain  all  the  mem- 
bers of  each  trade  in  the  trade  to  which  he 
belongs.  For  this  purpose  they  not  only  aid 
all  their  brethren  who  are  in  distress,  but  they 
use  every  exertion  to  retain  within  their  circle 
all  the  talent  and  all  the  wealth  which  has 
originated  among  them.  Their  public  institu- 
tions, libraries  and  lecture  rooms,  their  scienti- 
fic collections,  their  pictures  and  models,  afford 
the  means  of  gratifying  the  most  refined  taste ; 
and  these  and  the  tone  which  is  imparted  to 
their  circle  of  society  by  this  noble  esprit  de 
corps,  make  it  wholly  unnecessary  for  the  most 
imbitious  person  to  leave  the  trade  in  pursuit 
of  any  of  these  objects.  Any  one  may  see 
that  under  such  circumstances  it  is  a  nobler  ob- 
ject of  ambition  to  be  highly  respected  in  the 
trade,  than  can  be  attained  by  means  of  any 
position  out  of  it.  The  same  principle  holds 
good  under  all  circumstances.  If  a  man  has 
surrounded  himself  with  all  the  elegancies  and 
luxuries  which  affluence  can  purchase  by  dili- 
gence and  industry  in  his  trade,  he  should 


196  THE  YOUNG  MECHANIC. 

never  abandon  it  under  the  impression  that  he 
will  thus  elevate  himself  in  the  estimation  of 
his  fellow  citizens,  by  putting  on  a  finer  coat, 
and  appearing  in  a  different  character.  Such  a 
course  calls  down  a  torrent  of  invidious  remarks, 
not  from  his  brethren  of  the  trade,  who  are 
content,  for  the  most  part,  to  regret  the  deser- 
tion in  silence,  but  the  rest  of  that  little  world 
by  whose  Argus  eyes  the  movements  of  each 
individual  in  society  is  watched.  On  the  other 
hand,  the  mechanic  who  remains  attached  to 
his  trade,  when  it  is  no  longer  absolutely  ne- 
cessary for  his  support,  is  universally  respected 
for  this  mark  of  steadiness,  constancy  and  good 
sense.  In  connection  with  this  part  of  my 
subject,  I  am  strongly  reminded  of  an  old  ac- 
quaintance of  my  own,  in  the  old  common- 
wealth of  Massachusetts,  who  evidently  takes 
an  honest  pride  in  his  adherence  to  that  trade 
which  has  long  since  given  him  the  most  ample 
means  of  luxury  and  ease.  This  gentleman  is 
referred  to  by  Governor  Everett,  in  one  of  his 
recent  public  addresses,  in  the  following  terms: 
"  I  scarce  know  if  I  may  venture  to  adduce 
an  instance,  nearer  home,  of  the  most  praise- 
worthy and  successful  cultivation  of  useful 
knowledge,  on  the  part  of  an  individual  with- 


THE  ENLIGHTENED  MECHANIC.  ^97 

out  education,  busily  employed  in  mechanical 
industry.  I  have  the  pleasure  to  be  acquainted, 
in  one  of  the  neighbouring  towns,  with  a 
person,  who  was  brought  up  to  the  trade 
of  a  leather-dresser,  and  has  all  his  life  work- 
ed, and  still  works,  at  this  business.  He  has 
devoted  his  leisure  hours,  and  a  portion  of 
his  honourable  earnings,  to  the  cultivation 
of  useful  and  elegant  learning.  Under  the 
same  roof,  which  covers  his  store  and  work- 
shop, he  has  the  most  excellent  library  of  Eng- 
lish books,  for  its  size,  with  which  I  am  ac- 
quainted. The  books  have  been  selected  with 
a  good  judgment,  which  would  do  credit  to  the 
most  accomplished  scholar,  and  have  been  im- 
ported from  England  by  himself.  What  is 
more  important  than  having  the  books,  their 
proprietor  is  well  acquainted  with  their  contents. 
Among  them  are  several  volumes  of  the  most 
costly  and  magnificent  engravings.  Connected 
with  his  library,  is  an  exceedingly  interesting 
series  of  paintings,  in  water-colours,  which  a 
fortunate  accident  placed  in  his  possession,  and 
several  valuable  pictures,  purchased  by  himself. 
The  whole  form  a  treasure  of  taste  and  know- 
ledge, not  surpassed,  if  equalled,  by  any  thing 
of  its  kind  in  the  country." 


198  THE  YOUNG  MECHANIC 

Governor  Everett  might  have  added  thai  the 
leading  traits  in  Mr.  Dowsers  character  are 
sound  sense  and  good  taste ;  and  no  more  de- 
cisive proof  of  these  characteristics  could  be 
given  than  his  steady  adherence  to  his  original 
business.  In  the  same  address  from  which  the 
above  paragraph  is  quoted,  the  eloquent  orator 
urges  upon  his  hearers  that  every  working  man 
should  cultivate  his  mind  to  the  utmost  of  his 
ability ;  and  he  quotes  examples  of  many  who 
have  thus  raised  themselves  to  conspicuous 
offices  and  honours.  I  would  urge  upon  all 
working  men  the  same  duty  of  mental  cultiva- 
tion, not  as  affording  the  opportunity  of  aban- 
doning their  trade ;  but  as  giving  them  the 
means  of  dignifying  and  embellishing  it.  Lo- 
renzo de  Medicis  by  commerce  raised  his  family 
to  princely  rank — they  were  the  merchant  kings 
of  their  age.  The  American  mechanic  has  no 
occasion  to  seek  any  advancement  of  this  sort, 
for  every  voter  in  our  country  is  something 
greater  than  a  king ;  by  virtue  of  the  elective 
franchise  he  is  a  maker  of  kings.  When  I 
speak  of  adhering  to  one's  trade,  J' would  by 
no  means  be  understood  to  lay  down  a  rule 
without  exceptions.  Emergencies  may  occur 
which  shall  render  it  a  paramount  duty  to  entel 


DUTY  OF  WORKING  MEN.  |gg 

upon  a  new  and  difficult  profession.  The  me- 
chanic, like  any  other  citizen,  may  be  suddenly 
called  upon  to  shoulder  his  musket  and  defend 
his  country  from  invasion,  as  happened  in  the 
case  of  General  Greene ;  or  he  may  be  required 
to  aid  the  same 'great  cause  by  his  wisdom  in 
council,  as  in  the  case  of  Sherman  and  Frank- 
lin. When  a  country  is  to  be  saved  by  valour 
or  Avisdom,  it  becomes  a  matter  of  absolute 
necessity  that  the  working  men  should  contri- 
bute a  large  contingent  towards  the  grand  army 
of  defence  as  well  as  the  council  of  the  nation. 
For  a  time,  at  least,  a  new  course  of  life  must 
then  be  embraced.  But  the  greatest,  and  most 
celebrated  among  those  who  have  been  detach- 
ed from  their  trade  in  this  or  in  any  other  way, 
have  always  shown  an  honest  pride  in  their 
original  calling.  Girard  wrote,  himself  mariner 
in  his  will ;  and  Franklin  called  himself  printer 
in  his  epitaph. 


200  THE  YOUNG  MECHANIC. 


CHAPTER  III. 

THE  MECHANIC  SHOULD  HONOUR  HIS 
TKADE. 

I  HAVE  already  insisted  that  the  mechanic 
in  order  to  be  useful,  happy  and  respectable, 
should  become  a  thorough  master  of  his  trade, 
and  should  remain  attached  to  it.  1  would  in 
the  next  place  urge  upon  him  the  duty  and 
policy  which  dictate  that  he  should  honour  his 
trade.  Tlrere  are  two  ways  in  which  this  may 
be  done  :  first,  by  seeking  distinction  in  it;  and 
secondly,  by  adorning  it  with  intellectual  re- 
creations. 

The  love  of  distinction  is  common  to  nearly 
all  men  ;  and  the  most  remarkable  and  conspi 
cuous  diversities  of  character  are  produced  by 
the  different  modes  in  which  this  favourite  ob 
ject  is  pursued.  One  man  seeks  it  by  brillian/ 
deeds  in  the  public  service,  another  by  munifi 
cent  institutions.  Here  we  see  distinction 
courted  by  eloquence,  and  there  by  learning 
Some  hope  to  become  distinguished  by  their 
,  literary  efforts,  or  their  scientific  discoveries, 
while  others,  with  a  less  laudable,  but  not  les* 


LOVE  OF  DISTINCTION  £01 

earnest  ambition,  seek  to  attract  public  atten* 
tion  by  mere  eccentricity  of  character  or  extra- 
vagance in  conduct,  dress  or  equipage.  Doubt- 
less this  passion,  so  generally  prevalent  among 
men,  has  been  implanted  in  the  human  breast 
for  a  wise  and  useful  purpose ;  and  it  is  there- 
fore right  to  allow  it  a  field  for  action,  provided 
that  field  be  a  safe  and  honourable  one.  If  this 
postulate  be  granted,  I  would  ask  what  could 
afford  a  fairer  and  nobler  field  for  any  man^s 
ambition,  than  the  pursuit  of  distinction  by  ex- 
traordinary excellence  in  his  trade  or  profes- 
sion. Each  of  the  mechanical  trades  affords 
ample  room  for  the  exercise  of  ingenuity  in 
the  improvement  of  its  processes,  and  the  con- 
sequent improvement  of  its  products ;  and  the 
free  institutions  and  abundant  resources  of  our 
country,  and  the  ease  with  which  the  workman 
may  support  himself,  has  already  enabled  Ame- 
rican industry  and  invention  in  many  instances 
to  claim  the  admiration  of  the  world.  It  must 
be  a  proud  reflection  to  the  American  mechanic, 
that  one  of  his  class  has  exacted  the  most  un- 
equivocal homage  to  the  genius  of  our  country 
from  the  proud  Sultan  of  the  East,  by  his  won- 
derful skill  as  a  naval  constructor ;  and  every 
Philadelphian  may  justly  entertain  a  feeling  oi 


202  THE  YOUNG  MECHANIC 

exultation  when  he  remembers  that  a  mechanic 
of  one  of  our  cities  is  at  this  moment  furnishing 
locomotive  engines,  acknowledged  to  be  supe- 
rior to  all  others,  for  the  use  of  British  and 
Austrian  rail  road  companies.  Such  distinction 
as  this  we  must  acknowledge  to  be  fairly  and 
honourably  won.  It  is  true  that  all  may  not 
hope  to  rise  so  high  in  the  world's  estimation 
as  to  attract  applause  from  foreign  countries. 
But  every  one  may  reap  the  reward  of  diligence, 
ingenuity  and  devotion  to  his  business,  in  the 
applause  of  that  valued  circle,  which  is,  in  a 
certain  sense,  ail  the  world  to  him — the  circle 
of  his  associates  and  friends. 

Again,  the  mechanic  may  honour  his  trade 
by  adorning  it  with  intellectual  recreations.  It 
is  not  desirable,  in  fact  it  is  not  possible  for  a 
man  to  devote  every  moment  of  his  time  to  the 
business  by  which  he  lives.  Such  intense  ap- 
plication is  injurious  both  to  the  body  and  the 
mind.  It  destroys  health,  racks  the  brain,  and 
ruins  the  temper.  The  repose  of  the  domestic 
circle,  the  quiet  hour  for  reading  or  music,  or 
relaxation  of  some  other  kind,  seems  absolutely 
necessary  for  the  preservation  of  that  greatest 
of  earthly  blessings — a  sound  mind  in  a  healthy 
body.  The  business  of  the  mechanic  is  pre- 


EXAMPLE  OF  CHARLES  LAMB.  203 

cisely  that  which  renders  it  most  expedient  foi 
birn  to  give  his  recreations  an  intellectual  cast ; 
and  it  is  owing  to  the  circumstance  that  the 
alternation  of  mental  and  bodily  labour  is  best 
suited  to  the  human  constitution,  that  some  of 
the  most  beautiful  and  brilliant  productions  of 
the  human  intellect  have  proceeded  from  those 
persons  who  were  compelled,  for  many  hours 
of  each  day,  to  labour  at  a  business  which  was 
purely  mechanical.  Cast  your  eye  over  the 
whole  field  of  English  literature,  and  see  who 
it  is  that  has  brought  the  art  of  essay  writing 
to  its  greatest  perfection.  Of  course  you  in- 
stantly answer,  Charles  Lamb.  He  is  univer- 
sally acknowledged  to  be  in  this  department 
inimitable,  unrivalled,  unapproachable.  The 
best  critics  say  that  we  can  never  hope  to  see 
such  essays  produced  by  any  other  writer. 
Yet  these  beautiful  productions  were  the  work 
of  leisure  evenings.  The  composition  of  them 
served  as  a  relaxation,  after  severe  labour 
through  the  day  at  the  India  House  in  copy- 
ing commercial  papers,  which  to  him  must  have 
been  a  perfectly  mechanical  operation.  Never- 
theless, he  had  the  good  sense  to  adhere  to  this, 
his  trade,  long  after  he  was  one  of  the  most 
famous  writers  in  England,  and  in  fact  until  hi* 
18 


204  THE  YOUNG  MECHANIC. 

age  and  services  entitled  him  to  a  retiring  pen 
sion.  I  will  not  weary  your  patience  by  citing 
other  examples,  although  there  are  thousands  at 
hand,  in  proof  of  my  position  that  intellectual 
recreations  are  particularly  appropriate  for  the 
mechanic,  and  that  they  form  the  proper  and 
legitimate  ornament  of  his  trade. 

Coleridge,  an  author  by  profession,  tells  us 
in  plain  terms  that  it  is  necessary,  in  order  to 
be  successful  in  works  of  imagination,  to  have 
some  profession  or  trade  which  is  to  a  certain 
extent  mechanical,  and  he  allectionately  exhorts 
all  young  people  to  avoid  his  own  profession 
if  they  would  be  useful  and  happy.  I  cite  his 
observations,  which  are  as  remarkable  as  they 
are  just. 

u  An  interest  in  the  welfare  of  those  who,  at 
the  present  time,  may  be  in  circumstances  not 
dissimilar  to  my  own  at  my  first  entrance  into 
life,  has  been  the  constant  accompaniment,  and, 
(as  it  were,)  the  under-song  of  all  my  feelings. 
Whitehead,  exerting  the  prerogative  of  his  lau- 
reateship,  addressed  to  youthful  poets  a  poetic 
charge,  wh:ch  is  perhaps  the  best,  and  certainly 
the  most  interesting  of  his  works.  With  no 
other  privilege  than  that  of  sympathy  and  sin- 
cere good  wishes*  I  would  address  an  affectionate 


TRADE  OF  AUTHORSHIP.  205 

exhortation  to  the  youthful  literati,  grounded  on 
my  own  experience,  it  will  be  but  short ;  for 
the  beginning,  middle,  and  end,  converge  to  one 
charge:  Never  pursue  literature  as  a  trade, 
With  the  exception  of  one  extraordinary  man,  I 
have  never  known  an  individual,  least  of  all,  an 
individual  of  genius,  healthy  or  happy  without 
a  profession,  i.  e.  some  regular  employment 
which  does  not  depend  on  the  will  of  the  mo- 
ment, and  which  can  be  carried  on  so  far  me- 
chanically, that  an  average  quantum  only  of 
health,  spirits,  and  intellectual  exertion,  are 
requisite  to  its  faithful  discharge.  Three  hours 
of  leisure,  unannoyed  by  any  alien  anxiety, 
and  looked  forward  to  with  a  delight  as  a 
change  and  recreation,  will  suffice  to  realize  in 
literature,  a  larger  product  of  what  is  truly 
genial,  than  weeks  of  compulsion.  Money  and 
immediate  reputation,  form  only  an  arbitrary 
and  accidental  end  of  literary  labour.  The 
hope  of  increasing  them,  by  any  given  exertion, 
will  often  prove  a  stimulant  to  industry ;  but 
the  necessity  of  acquiring  them  will,  in  all 
works  of  genius,  convert  the  stimulant  into  a 
narcotic.  Motives  by  excess  reverse  ttoeir  very 
nature,  and,  instead  of  exciting,  stun  and  stu- 
pify  the  mind.  For  it  is  one  contradistinction 


2QQ  THE  YOUNG  MECHANIC. 

of  genius  from  talent,  that  its  predominant 
end  is  always  compromised  in  the  means ;  and 
this  is  one  of  the  many  points  which  establish 
an  analogy  between  genius  and  virtue.  Now, 
though  talents  may  exist  without  genius,  yet, 
as  genius  cannot  exist,  certainly  not  manifest 
itself,  without  talents,  I  would  advise  every 
scholar  who  feels  the  genial  power  working 
within  him,  so  far  to  make  a  division  between 
the  two,  that  he  should  devote  his  talents  to 
the  acquirement  of  competence  in  some  known 
trade  or  profession,  and  his  genius  to  objects 
of  his  tranquil  and  unbiassed  choice ;  while  tlu* 
consciousness  of  being  actuated  in  both  alike 
by  the  sincere  desire  to  perform  his  duty,  will 
alike  ennoble  both.  My  dear  young  friend,  (I 
would  say,)  '  suppose  yourself  established  in 
any  honourable  occupation.  From  the  manu- 
factory, or  counting-house,  from  the  law  court, 
or  from  having  visited  your  last  patient,  you 
return  at  evening — 

Dear  tranquil  time,  when  the  sweet  sense  of  home 
Is  sweetest — 

to  your  family,  prepared  for  its  social  enjoy- 
ments, with  the  very  countenances  of  your  wife 
and  children  brightened,  and  their  voice  of 
welcome  made  doubly  welcome  by  the  know- 


TRADE  OF  AUTHORSHIP.  £0? 

ledge  that,  as  far  as  they  are  concerned,  you 
have  satisfied  the  demands  of  the  day,  by  the 
labour  of  the  day.  Then  when  you  retire  into 
your  study,  in  the  books  on  your  shelves  you 
revisit  so  many  venerable  friends  with  whom 
you  can  converse.  Your  own  spirit,  scarcely 
less  free  from  personal  anxieties  than  the  great 
minds  that,  in  those  books,  are  still  living  for 
you  !  Even  your  writing  desk  with  its  blank 
paper,  and  all  its  other  implements,  will  appear 
as  a  chain  of  flowers,  capable  of  linking  your 
feelings,  as  well  as  thoughts,  to  events  and  cha- 
racters past  or  to  come ;  not  a  chain  of  iron, 
which  binds  you  down  to  think  of  the  future, 
and  the  remote,  by  recalling  the  claims  and 
feelings  of  the  preremptory  present.  But  why 
should  I  say  retire  ?  The  habits  of  active  life 
and  daily  intercourse  with  the  stir  of  the  world, 
will  tend  to  give  you  such  self-command,  that 
the  presence  of  your  family  will  be  no  inter- 
ruption. Nay,  the  social  silence  or  undisturb- 
ing  voices  of  a  wife  or  sister,  will  be  like  a 
restorative  atmosphere,  or  soft  music,  which 
moulds  a  dream  without  becoming  its  object 
If  facts  are  required,  to  prove  the  possibility  of 
combining  weighty  performances  in  literature 
with  lull  and  independent  employment,  the 
IS* 


208  TIIE  YOUNG  MECHANIC. 

works  of  Cicero  and  Xenophon  among-  the 
ancients,  of  Sir  Thomas  More,  Bacon,  Baxter, 
or,  to  refer,  at  once,  to  later  and  contemporary 
instances,  Darwin  and  Roscoe,  are  at  once  deci- 
sive of  the  question. 

"  Whatever  be  the  profession  or  trade  chosen, 
the  advantages  are  many  and  important,  com- 
pared with  the  state  of  a  mere  literary  man, 
who,  in  any  degree,  depends  on  the  sale  of  his 
works  for  the  necessaries  and  comforts  of  life. 
In  the  former,  a  man  lives  ip  sympathy  with 
the  world  in  which  he  lives.  At  least,  he  ac- 
quires a  better  and  quicker  tact  for  the  know- 
ledge of  that  with  which  men  in  general  can 
sympathize.  He  learns  to  manage  his  genius 
more  prudently  and  efficaciously.  His  powers 
and  acquirements  gain  him  likewise  more  real 
admiration,  for  they  surpass  the  legitimate  ex- 
pectation of  others.  He  is  something  besides 
an  author  and  is  not  therefore  considered 
merely  as  an  author.  The  hearts  of  men  are 
open  to  him,  as  to  one  of  their  own  class ;  and 
whether  h^  exerts  himself  or  not  in  the  con 
versational  circles  of  his  acquaintance,  his 
silence  is  not  ettrbuted  to  pride,  nor  his  com- 
municativenes0  to  vanity.  To  these  advantages 
I  will  venture  tc  add  a  superior  chance  of  hap- 


TRADE  OF  AUTHORSHIP. 

piness  in  domestic  life,  were  it  only  that  it  is  as 
natural  for  the  man  to  be  out  of  the  circle  of 
his  household  during  the  day,  as  it  is  merito- 
rious for  the  woman  to  remain  for  the  most 
part  within  it.  But  this  subject  involves  points 
of  consideration  <*o  numerous  and  so  delicate, 
and  would  not  only  permit,  but  require  such 
ample  documents  from  the  biography  of  literary 
men,  that  I  now  merely  allude  to  it  in  transitu. 
When  the  same  circumstance  has  occurred  at 
very  different  times  to  very  different  persons, 
ill  of  whom  have  some  one  thing  in  common, 
there  is  reason  to  suppose  that  such  circum- 
stance is  not  merely  attributable  to  the  persons 
concerned,  but  is  in  some  measure  occasion- 
ed by  the  one  point  in  common  to  them  all. 
Instead  of  the  vehement  and  almost  slanderous 
dehortation  from  marriage,  which  the  4Miso- 
gyne  Boccaccio'  ( Vita  e  Coslumi  di  Dante,  p. 
12.  16)  addresses  to  literary  men,  I  would 
substitute  the  simple  advice :  be  not  merely  a 
man  of  letters !  Let  literature  be  an  honour- 
able augmentation  to  your  arms,  but  not  con- 
stitute the  coat,  or  fill  the  escutcheon ! 

"  It  would  be  a  sort  of  irreligion,  and  scarce- 
ly less  than  a  libel  on  human  nature,  to  believe 
that  there  is  any  established  and  reputable  pro- 


210  THE  YOUNG  MECHANIC. 

fession  or  employment,  in  which  a  man  may 
not  continue  to  act  with  honesty  and  honour; 
and,  doubtless,  there  is  likewise  none  which 
may  not  at  times  present  temptations  to  the 
contrary.  But  wofully  will  that  man  find  him- 
self mistaken,  who  imagines  that  the  profession 
of  literature,  01  (to  speak  more  plainly)  the 
trade  of  authorship,  besets  its  members  with 
fewer  or  with  less  insidious  temptations,  than 
the  church,  the  law,  or  the  different  branches 
of  commerce.' " 

Charles  Lamb  himself  subscribes  to  this 
opinion  of  Coleridge,  and  urges  it  upon  one  of 
his  friends  with  great  force ;  and  Herder  is 
quoted  by  Coleridge  in  support  of  his  own 
opinion,  as  follows : 

Translation. — u  With  the  greatest  possible 
solicitude  avoid  authorship.  Too  early,  or  im- 
moderately employed,  it  makes  the  head  waste 
and  the  heart  empty,  even  were  there  no  other 
worse  consequences.  A  person  who  reads  only 
to  print,  in  all  probability  reads  amiss ;  and  he 
who  sends  away  through  the  pen  and  the  press, 
every  thought,  the  moment  it  occurs  to  him. 
will  in  a  short  time  have  sent  all  away,  am) 
will  become  a  mere  journeyman  of  the  printing 
office,  a  compositor." 


NECESSITY  OF  A  TRADE.  Ql] 

So  much  for  the  opinion  of  great  authors  on 
ft.e  character  of  their  trade. 

In  all  these  observations  you  find  it  distinctly 
admitted  that  the  fancy,  the  imagination,  the 
creative  powers  of  the  mind  are  not  to  be  taxed 
for  the  purposes  of  mere  support.  They  say 
it  is  better  to  work  for  a  living  at  some  business 
which  is  mechanical,  by  way  of  a  regular  trade 
or  profession,  and  to  give  the  genius  free  ptay 
in  the  hours  of  recreation.  That  such  a  dis- 
tribution of  one's  time  may  produce  the  hap- 
piest effect  is  abundantly  apparent  from  the 
experience  of  all  ages.  Without  adverting  to 
the  busy  life  led  by  Cicero  and  Quinetilian, 
whom  I  esteem  among  the  best  authors  of  an- 
cient times,  we  may  conie  down  at  once  to  the 
moderns.  Bacon,  the  prince  of  philosophers, 
was  a  lawyer  laboriously  active  in  his  profes- 
sion during  the  greater  part  of  his  life  ;  Shaks- 
peare,  the  most  admirable  of  all  writers,  was  a 
player  and  manager,  and  was  obliged  to  work 
hard  at  the  mechanical  part  of  these  laborious 
employments  ;  Raleigh  was  a  soldier  and  states- 
man, one  of  the  most  active  of  his  age ;  Cla- 
rendon was  a  busy  statesman  and  lawyer;  Addi- 
son  was  secretary  of  state  while  he  ,vas  writing 
the  Spectator;  Walter  Scott  was  a  writer  for 


212  THE  YOUNG  MECHANIC. 

the  signet,  and  sheriff  of  the  county ;  and  it  is 
a  curious  fact  that  this  writer,  the  most  prolific 
as  well  as  the  best  of  our  century,  passed  his 
days  in  bodily  labour,  riding  about  the  county 
or  working  at  his  profession.  It  was  remarked 
that  nobody  could  conjecture  when  it  was  that 
he  found  time  to  write  his  voluminous  works. 

if  we  come  to  our  own  country,  the  exam- 
ples are  more  numerous.  All  our  best  authors 
are  working  men.  Prescott  is  a  lawyer ;  Ban- 
croft, a  teacher  for  some  years,  and  afterwards 
collector  of  the  port  of  Boston ;  Charles  Sprague 
is  a  bank  clerk;  Halleck  collects  Mr.  Astor's  • 
rents  ;  Dana  is  a  lawyer;  Longfellow,  a  teacher. 
In  fact,  with  us,  authorship  is  seldom  a  profes- 
sion. Most  of  our  literature  has  been  produced 
in  the  leisure  hours  rescued  from  laborious  oc- 
cupations. 

Our  scientific  and  useful  inventions  too  have 
generally  resulted  from  the  very  course  which 
I  am  desirous  to  recommend  to  the  mechanic, 
viz. :  that  of  honouring  his  trade  by  adorning 
it  with  intellectual  recreations.  Fulton  was  a 
portrait  painter,  who  amused  himself  in  his  idle 
hours  with  experiments  on  steam  power ;  Whit- 
ney, the  inventor  of  the  cotton  gin,  was  a  ma- 
chinist, whose  judicious  employment  of  his 


AMERICAN  AUTHORS. 

leisure  moments  led  him  to  an  invention  which 
has  trebled  the  value  of  cotton  lands  at  the 
South;  Whittemore,  of  West  Cambridge,  who 
invented  the  machinery  for  the  manufacture  of 
cards,  was,  if  1  recollect  right,  a  cabinet  maker. 
The  case  of  Franklin  is  familiar  to  all. 

All  these  examples  tend  to  establish  the  same 
truth, — that  a  mechanical  business,  a  life  of  acti- 
vity and  labour,  is  far  from  being  unfavourable 
to  the  highest  operations  of  the  intellect ;  and 
that  relaxation  from  active  labours  is  most  ap- 
propriately found  ia  mental  recreations. 


214  THE  YOUNG  MECHANIC. 


CHAPTER  IV 

THE  MECHANIC  SHOULD  DEVOTE  HIS  LEI- 
SURE TO  THE  GENERAL  INTERESTS  OF 
HIS  TRADE. 

ONE  more  duty  I  would  urge  upon  the  me- 
chanic, in  order  to  the  finishing  of  his  charac- 
ter of  a  useful,  happy  and  respectable  man. 
Having  attained  wealth  at  the  time  of  life  when 
it  is  desirable  to  cease  from  active  labour,  I 
would  have  him  devote  himself  to  the  general 
interests  of  his  trade. 

There  are  many  ways  in  which  the  wealthy 
mechanic  may  promote  the  general  interests  of 
his  trade,  when  he  has  retired  from  all  partici- 
pation in  its  labours  or  profits. 

He  may  give  a  tone  to  its  society  by  exer- 
cising a  refined  and  judicious  hospitality.  lit 
may  make  his  house  the  resort  of  kindred  spi- 
rits, who  will  unite  with  him  in  their  endeavours 
to  retain  men  of  talent  and  influence  in  the 
trade.  He  may  assist  young  men  who  are  en- 
tering upon  business  for  themselves  with  money, 
credit  and  good  advice.  He  may  save  many  a 
brother  from  ruin  by  interposing  a  friendly 


FRANKLIN.  215 

voice,  and  a  helping  hand  at  the  critical  moment 
when  they  are  most  needed.  He  may  become 
in  his  old  age  the  Mecaenas,  as  well  as  the 
Nestor  of  his  fraternity,  by  patronizing  the  in- 
tellectual efforts  of  their  leisure  hours. 

Such  was  the  course  of  Franklin;  and  his 
munificent  aid  ceased  not  with  his  life.  In  his 
will  a  permanent  fund  was  established  for  aiding 
the  young  mechanics  of  his  native  place  by  loans 
of  money.  The  example  of  his  life,  however, 
has  been  of  more  value  than  a  legacy  of  millions. 
He  was  a  mechanic  who  fulfilled  the  several 
conditions  which  we  have  been  considering  as 
necessary  to  happiness,  usefulness  and  respect- 
ability. He  made  himself  a  thorough  master 
of  his  trade ;  he  adhered  to  it  till  the  impera- 
tive call  of  his  suffering  country  compelled  him 
to  relinquish  it ;  and  he  honoured  his  trade  by 
seeking  distinction  in  it,  and  by  adorning  it 
with  intellectual  recreations.  Long  may  his 
example  be  imitated  by  his  countrymen — long 
may  his  race  live  and  flourish  in  the  land. 
Such  mechanics  are  the  bulwark  of  our  free 
institutions.  While  we  have  men  of  the  Frank- 
lin stamp  among  us,  we  shall  never  want  a 
supply  of  heroes  and  statesmen  to  perform  great 
and  brilliant  actions,  or  poets,  historians  and 

orators  to  celebrate  them. 
19 


216  THE  YOUNG  MECHANIC. 


CHAPTER  V. 

MISDIRECTION  OF  INDUSTRY— PREJUDICES 
AGAINST  THE  MECHANICAL  TRADES. 

AMONG  the  many  causes  which  have  led  "to 
the  present  depressed  state  of  affairs  in  oui 
country,  there  is  one  which  appears  to  me  an 
efficient  one,  although  it  has  been  in  a  great 
measure  overlooked.  This  is  the  misdirection 
of  industry — of  productive  labour.  All  obser- 
vers readily  perceive  that  capital  has  been 
thrown  away ;  few  take  notice  of  the  fact  that 
hands  and  heads  have  been  employed  on  works 
that  are  now  known  to  be  utterly  useless. 
Railroads,  for  example,  have  been  constructed, 
which  can  never,  by  any  possibility,  be  re- 
quired for  the  public  accommodation  to  such 
an  extent  as  to  pay  the  expense  of  keeping 
them  in  repair  and  employing  lines  of  cars 
upon  them.  Mines  have  been  opened  and 
wrought  in  situations  where  no  veins  of  metal 
existed,  although  the  imaginations  of  the  stock- 
holders, aided  by  the  fine  stories  of  some  cun- 
ning Dousterswivel,  had  made  each  of  the  re- 


MISAPPLICATION  OF  TIME  AND  TALENTS.  217 

gions  a  perfect  El  Dorado.  Even  agricultural 
labour  has  been  misapplied  ;  for  trees  have  been 
planted  and  nursed  with  the  greatest  care,  un- 
der the  impression  that  their  leaves  were  to  be 
converted  into  silks  which  should  rival  the 
fabrics  of  Lyons  and  Benares ;  and  yet  these 
very  trees  have  subsequently  been  cut  down  as 
cumberers  of  the  ground. 

The  productive  industry  of  this  country  might 
just  as  well  have  been  employed  in  the  con- 
struction of  pyramids,  like  those  of  the  ancient 
Egyptians,  as  on  works  of  this  nature.  It  is 
literally  labour,  time,  and  talents  thrown  away. 

But  these  are  not  the  only  ways  in  which 
labour,  time  and  talent  have  been  misdirected. 
Thousands  of  our  young  men  have  entered  the 
learned  professions  when  they  were  already 
crowded,,  and  are  consequently  wasting  their 
lives  in  vain  hopes ;  and  other  thousands  have 
devoted  themselves  to  the  pursuits  of  com- 
merce without  capital,  prudence,  or  intelligence 
sufficient  to  avoid  the  dangers  of  commercial 
enterprize ;  and  these  men  are  now  either  bank- 
rupts, or  involved  in  a  series  of  embarrassments 
v^hich  may  last  through  their  whole  lives.  An 
error  in  the  choice  of  one's  profession  is  one 
which  3  followed  by  painful  consequences,  as 


2  1  S  THfi  YOUNG  MECHANIC. 

many  have  found  to  their  cost.  In  this  coun- 
try we  are  apt  to  be  too  ambitious  and  restless. 
The  freedom  of  our  institutions,  instead  of  im- 
pressing upon  us  the  wholesome  lesson  that  all 
men  are  naturally  equal  in  dignity,  and  that 
consequently  every  trade  and  profession  may 
be  ennobled  by  the  personal  merit  of  its  mem- 
bers, leads  men  to  aspire  to  certain  professions 
which  they  esteem  genteel ;  and  to  high  offices 
which  the  constitution  has  made  attainable  by 
citizens  of  all  classes. 

This  is  wrong.  An  American  should  respect 
himself.  A  citizen  of  this  republic  should  deem 
himself  a  peer  of  the  world — one  of  nature's 
noblemen.  He  should  consider  that  the  cir- 
cumstance of  his  being  an  American  citizen  is 
sufficient  to  adorn  with  all  proper  dignity  any 
trade  or  profession  which  he  may  adopt. 
Having  settled  this  point  with  himself,  he  is 
left  at  perfect  liberty  to  look  around  with  ^an 
unprejudiced  mind,  upon  the  different  modes 
of  obtaining  subsistence  and  making  himself 
useful  to  the  community ;  and  he  can  make  his 
choice  upon  the  same  principles  that  should 
govern  him  in  deciding  any  practical  question. 
In  taking  a  survey  of  some  large  community 
with  reference  to  the  success  which  has  attend- 


MECHANICS  AND  MERCHANTS.      219 

ed  the  exertions  of  other  men,  in  order  to  aid 
his  judgment  in  the  choice  of  a  profession,  the 
youth  or  his  adviser  may  peradventure,  arrive 
at  some  results  which  he  did  not  anticipate. 

Suppose,  for  example,  that  he  should  examine 
the  comparative  success  of  those  men  whom 
we  know  to  have  devoted  themselves  to  me- 
chanical  trades,  and  those  who  have  become 
merchants.  Would  it  not  be  apparent  that  where 
one  mechanic  has  failed  and  caused  extensive 
losses  to  his  friends  and  the  community,  ten 
merchants  have  done  the  same  thing  ?  On  the 
other  hand,  would  it  not  appear  that  where  one 
merchant  had  acquired  a  competent  fortune  and 
retired  from  business  in  the  decline  of  life,  se- 
veral mechanics  have  done  the  same  thing  ?  If 
we  were  to  run  over  the  list  of  persons  taxed 
for  real  estate,  should  we  not  find  more  me- 
chanics than  merchants  living  in  their  own 
houses,  and  deriving  a  handsome  income  from 
their  rents ; 

If  it  be  said  that  this  not  a  fair  test  of  com- 
parative success,  let  another  be  resorted  to. 
Take  the  whole  number  of  persons  employed 
in  mechanical  trades,  and  the  whole  number  of 
persons  employed  in  commerce,  say  for  the  last 
twenty  years ;  then  calculate  what  per  centage 


THE  YOUNG  MECHANIC. 

of  each  class  has  failed,  what  per  eentage  has 
gained  a  decent  subsistence  without  failing,  and 
what  per  eentage  has  arrived  at  what  is  called 
independence.  The  result  of  such  an  inquiry 
would  satisfy  the  inquirer  that  it  is  a  safer 
course  to  become  a  mechanic  than  to  be  a 
merchant. 

The  prejudice  against  the  mechanical  trades 
is  a  relic  of  feudalism  unworthy  of  our  free 
country.  Considered  with  reference  to  those 
old  feudal  prejudices,  ail  the  pursuits  by  which 
bread  is  earned  in  our  country  are  equally 
base.  Considered  in  the  light  of  republican 
philosophy,  they  are  all  equally  honourable. 
The  baron  of  the  middle  ages,  who  could  not 
read  or  write,  looked  down  upon  the  merchant, 
the  mechanic,  and  the  lawyer  with  equal  con- 
tempt; and  the  baron  of  modern  days,  who 
cannot  even  wield  a  lance,  considers  himself 
superior  to  the  greatest,  wisest,  and  best  of 
those  who  were  born  commoners.  These  old 
feudal  prejudices  are  ridiculous.  But  when  we 
call  one  profession  respectable^  and  another 
less  respectable,  do  we  not  adopt  them  ?  When 
we  talk  of  degrading  ourselves  by  making 
tradesmen  of  our  sons,  do  we  not  give  sanc- 
tion to  the  stupid  and  exploded  notions  of  the 


FEUDAL  PREJUDICES.  221 

dark  ages  ?  When  we  admit  that  any  citizen 
may  lose  caste  by  associating  with  any  other 
honest  and  honourable  man,  do  we  not  submit 
to  a  barbarism  worse  than  Gothic^the  bar- 
barism of  Hindostan  and  China  ? 

Such  notions  should  be  laid  aside  with  other 
useless  lumber,  as  unfit  for  an  age  and  a  coun- 
try where  common  sense  gives  law  to  society, 
and  where  real  merit  stamps  the  seal  of  respect- 
ability. It  is  but  fighting  shadows  to  offer  ar- 
guments in  opposition  to  such  views.  I  gladly 
turn  therefore  from  this  to  the  more  agreeable 
task  of  continuing  the  subject  of  my  last  lec- 
ture— the  mechanic. 


THE  YOUNG  MECHANIC. 


CHAPTER  VI. 

INTELLECTUAL  CULTIVATION  OF  THE 
MECHANIC— ITS  IMPORTANCE. 

I  PROPOSE  now  to  offer  a  few  remarks  on  the 
intellectual  cultivation  of  the  mechanic,  its  im- 
portance, its  means,  and  its  rewards. 

That  intellectual  cultivation,  as  a  means  of 
moral  and  social  elevation,  is  as  important  to 
the  mechanic  as  it  is  to  any  other  citizen,  is  a 
truth  so  obvious  as  not  to  require  argument  or 
illustration  for  its  support.  But  this  is  not  all 
He  has  stronger  reasons  for  study  than  most 
other  men.  His  very  livelihood  may  depend 
in  a  great  measure  on  a  degree  of  skill  in  his 
art  which  cannot  be  acquired  without  a  know- 
ledge of  the  scientific  principles  and  natural 
laws  on  which  the  arts  are  founded. 

The  whole  system  of  mechanics'  institutes, 
lyceums,  lectures,  and  collections  of  specimens 
and  machines,  is  nothing  more  nor  less  than  an 
open  confession  made  by  the  mechanics  them- 
selves, that  intellectual  cultivation  has  become 
absolutely  necessary,  in  order  that  they  may 


COMPETITION.  22*1 

keep  pace  with  the  spirit  of  the  age — an  ac- 
knowledgment that  the  time  has  come  when 
science  and  art  shall  be  firmly  united,  and  thy 
head  and  the  hands  shall  work  together. 

Competition  imposes  upon  the  mechanic  ot 
the  present  day  the  necessity  of  study.  Unless 
he  keeps  pace  with  the  intelligence  of  the  times, 
he  will  speedily  find  himself  working  at  a 
ruinous  disadvantage.  While  the  workman 
who  is  content  to  remain  stationary  in  scien 
tific  intelligence,  neglects  the  opportunities  of 
information  afforded  by  the  institute,  the  read- 
ing room,  and  a  constant  social  intercourse 
with  the  most  intelligent  of  his  trade;  his 
neighbour,  availing  himself  of  these  advantages, 
may  possess  himself  of  new  processes,  new 
materials,  or  new  facts,  which  will  enable  him 
to  reduce  his  prices,  and  in  a  great  measure  to 
carry  off  the  custom  of  the  place. 

It  was  not  always  thus.  Monopoly  and  pre- 
scription formerly  exerted  an  influence  as  inju- 
rious to  the  arts  as  that  which  is  now  exerted 
by  competition  is  beneficial. 

Indeed,  as  has  been  ably  shown  by  a  learned 
authority,*  much  mischief  has  been  occasioned 

*  Governor  Everett.     Oration,  p.  232. 


224:  THE  ^°IJNG  MECHANIC. 

in  past  times  by  the  ignorance  of  artizans.    He 
says  : — 

"  The  history  of  the  progress  of  the  human 
mind  shqws  us,  that  for  want  of  a  diffusion 
of  scientific  knowledge  among  practical  men, 
great  evils  have  resulted,  both  to  science  and 
practice.  Before  the  invention  of  the  art  of 
printing,  the  means  of  acquiring  and  circulating 
knowledge  were  few  and  ineffectual.  The  phi- 
losopher was,  in  consequence,  exclusively  a 
man  of  study,  who,  by  living  in  a  monastic 
seclusion,  and  by  delving  into  the  few  books 
which  time  had  spared, — particularly  the  works 
of  Aristotle  and  his  commentators, — succeeded 
in  mastering  the  learning  of  the  day ;  learning, 
mostly  of  an  abstract  and  metaphysical  nature. 
Thus,  living  in  a  world  not  of  practice,  but 
speculation,  never  bringing  his  theories  to  the 
test  of  observation,  his  studied  assumed  a  vi- 
sionary character.  Hence  the  projects  for  the 
transmutation  of  metals ;  a  notion  not  origi- 
nating in  any  observation  of  the  qualities  of 
the  different  kinds  of  metals,  but  in  reasoning, 
i  priori,  on  their  supposed  identity  of  sub- 
stance. So  deep  rooted  was  this  delusion,  that 
a  great  part  of  the  natural  science  of  the  mid- 
dle ages  consisted  in  projects  to  convert  the 


EVILS  OF  IGNORANCE.  225 

baser  metals  into  gold.  It  is  plain,  that  such  a 
project  would  no  more  have  been  countenanced 
by  intelligent,  well-informed  persons,  practi- 
cally conversant  with  the  nature  of  the  metals, 
than  a  project  to  transmute  pine  into  oak,  or 
fish  into  flesh. 

"  In  like  manner,  by  giving  science  wholly 
up  to  the  philosophers,  and  making  the  practical 
arts  of  life  merely  a  matter  of  traditionary  repeti- 
tion from  one  generation  to  another  of  uninform- 
ed artists,  much  evil  of  an  opposite  kind  was 
occasioned.  Accident,  of  course,  could  be  the 
only  source  of  improvement ;  and  for  want  of 
acquaintance  with  the  leading  principles  of 
mechanical  philosophy,  the  chances  were  inde- 
finitely multiplied  against  these  accidental  im- 
provements. For  want  of  the  diffusion  of  in 
formation  among  practical  men,  the  principles 
prevailing  in  an  art  in  one  place  were  unknown 
in  other  places ;  and  processes  existing  at  one 
period  were  liable  to  be  forgotten  in  the  lapse 
of  time.  Secrets  and  mysteries,  easily  kept  in 
such  a  state  of  things,  and  cherished  by  their 
possessor  as  a  source  of  monopoly,  were  so 
common,  that  mystery  is  still  occasionally  used 
as  synonymous  with  trade.  This  also  contri- 
buted to  the  loss  of  arts  once  brought  to  pet" 


226  THE  ^OUNG  MECHANIC. 

fe^tion,  such  as  that  of  staining  glass,  as  prac- 
tised in  the  middle  ages.  Complicated  ma- 
chinery was  out  of  the  question  ;  for  it  requires, 
for  its  invention  and  improvement,  the  union  of 
scientific  knowledge  and  practical  skill.  The 
mariner  was  left  to  creep  along  the  coast,  while 
the  astronomer  was  casting  nativities  ;  and  the 
miner  was  reduced  to  the  most  laborious  and 
purely  mechanical  processes,  to  extract  the 
precious  metals  from  the  ores  that  really  con- 
tained them,  while  the  chemist,  who  ought  to 
have  taught  him  the  method  of  amalgamation, 
could  find  no  use  for  mercury,  but  as  a  men- 
struum, by  which  baser  metals  could  be  turned 
into  gold, 

u  At  the  present  day,  this  state  of  things  is 
certainly  changed.  A  variety  of  popular  trea- 
tises and  works  of  reference  have  made  the 
great  principles  of  natural  science  generally 
accessible.  It  certainly  is  in  the  power  of  al- 
most every  one,  by  pains  and  time  properly 
bestowed,  to  acquire  a  decent  knowledge  of 
every  branch  of  practical  philosophy.  But 
still,  it  would  appear,  that,  even  now,  this  part 
of  education  is  not  on  the  right  footing.  Gene- 
rally speaking,  even  now,  all  actual  instruction 
in  the  principles  of  natural  science  is  confined 


EDUCATION  OF  MECHANICS.      227 

to  the  colleges ;  and  the  colleges  are,  for  the 
most  part,  frequented  only  by  those  intended 
for  professional  life.  The  elementary  know- 
ledge of  science  which  is  communicated  at  the 
colleges,  is  indeed  useful  in  any  and  every 
calling ;  but  it  does  not  seem  right  that  none 
but  those  intended  for  the  pulpit,  the  bar,  or 
the  profession  of  medicine,  should  receive  in- 
struction in  those  principles  which  regulate  the 
operation  of  the  mechanical  powers,  and  lie 
at  the  foundation  of  complicated  machinery; 
which  relate  to  the  navigation  of  the  seas,  the 
smelting  and  refining  of  metals,  the  composi- 
tion and  improvement  of  soils,  the  reduction 
to  a  uniform  whiteness  of  the  vegetable  fibre, 
the  mixture  and  application  of  colours,  the 
motion  and  pressure  of  fluids  in  large  masses, 
the  nature  of  light  and  heat,  the  laws  of  mag- 
netism, electricity,  and  galvanism.  It  would 
seem  that  this  kind  of  knowledge  was  more 
immediately  requisite  for  those  who  are  to  con- 
struct or  make  use  of  labour-saving  machinery, 
who  are  to  traverse  the  ocean,  to  lay  out  and 
direct  the  excavation  of  canals,  to  build  steam 
engines  and  hydraulic  presses,  to  work  mines, 
and  to  conduct  large  agricultural  and  manufac- 
Uiring  establishments.  Hitherto,  with  some 
20 


228  THE  YOUNG  MECHANIC. 

partial  exceptions,  little  has  been  done,  syste- 
matically, to  afford  to  those  engaged  in  those 
pursuits,  that  knowledge  which,  however  con- 
venient to  others,  would  seem  essenfial  to  them. 
There  has  been  scarce  any  thing,  which  could 
be  called  education  for  practical  life  ;  and  those 
persons  who,  in  the  pursuit  of  any  of  the  use 
ful  arts,  have  signalized  themselves  by  the  em 
ployment  of  scientific  principles  for  the  inven- 
tion of  new  processes,  or  the  improvement  of 
the  old,  have  been  self-educated  men." 

It  is  argued,  in  opposition  to  this  view  of  the 
matter,  that  the  greatest  discoveries  and  inven- 
tions have  oeen  produced  by  self-taught  men, 
or  by  accidental  circumstances,  and  that  educa- 
tion is  therefore  unnecessary  for  the  mechanic. 
The  fact  is  indisputable ;  but  the  argument 
founded  on  it  against  the  intellectual  cultiva- 
tion of  working  men,  is  not  sound.  Another 
fact  will  sufficiently  refute  it.  Before  education 
became  generally  diffused  among  mechanics, 
useful  discoveries  and  inventions  were  much 
rarer  than  they  are  at  present.  When  the  great 
mass  of  mechanics  could  neither  read  nor  write, 
the  progress  of  invention  was  exceedingly 
slow.  Now  it  is  astonishingly  rapid.  In  the 
middle  ages  great  discoveries  in  the  arts  were 


A  LIFE  OF  LABOUR.  £29 

made  at  the  rate  of  about  one  in  a  hundred 
years.  Now  they  are  made  almost  every  year. 
Within  the  range  of  our  own  recollection  two 
great  motive  powers,  unknown  before,  have 
been  rendered  available  in  the  arts  of  life,  and 
scarcely  a  month  passes  without  the  announce- 
ment of  some  new  contrivance  for  economizing 
the  labour  of  man.  This  fact  not  only  an- 
swers the  argument  already  cited,  but  acts  with 
tremendous  power  on  the  opposite  side  :  thus, 

The  increase  of  education  among  mechanics 
increases  the  number  of  discoveries  and  im- 
provements in  the  arts,  by  which  human  labour 
is  abridged.  This  increase  of  power  is  an  in- 
crease of  happiness.  It  elevates  the  mechanic 
in  the  scale  of  social  being,  and  adds  to  the 
comfort — the  essential  happiness  of  society. 
By  means  of  the  recent  improvements  in  the 
arts  effected  by  ingenious  and  educated  mecha- 
nics, the  amount  of  severe  bodily  labour  pre- 
viously imposed  on  that  class  of  men  is  greatly 
diminished ;  and  this  is  no  small  gain. 

"  We  read,"  says  a  shrewd  writer,  "  we  read 
in  many  authors  great  encomiums  on  a  life  of 
labour,  and  of  the  superior  blessings  of  peasants 
and  hard-working  men,  whose  temperate  and 
abstemious  lives  nit  jnly  make  them  enjoy  an 


230  THE  YOUNG  MECIiAWlC. 

uninterrupted  state  of  health,  but  throw  a 
crimson  on  their  cheeks,  and  give  a  vigour  to 
their  bodies,  the  sons  of  wealth  and  affluence, 
they  tell  us,  may  in  vain  sigh  for.  This  sounds 
well ;  but  I  own  I  am  doubtful  of  the  fact 

"  If  I  compare  the  working  part  of  mankind, 
who  fare  hard,  with  those  who  eat  and  drink 
of  the  *  good  things  of  the  earth,'  I  think  1  can 
discern  better  complexions,  choicer  animal  spi- 
rits, and  stronger  bodies  in  the  latter  than  in 
the  former.  Incessant  labour  and  coarse  and 
scanty  food,  have  certainly  a  tendency  to  weaken 
the  bodies  of  mankind,  and  wear  them  out  be- 
fore their  time ;  and  this  we  see  is  the  case. 
What  becomes  then  of  the  fine-spun  theories 
of  visionary  authors  who  so  greatly  extol  a 
laborious  life  ?  Why,  they  are  destroyed,  like 
other  cobweb  systems,  that  will  not  bear  hand- 
ling." 

Education  multiplies  the  inventions  which 
lighten  bodily  labour.  Education  among  me- 
chanics is,  therefore,  a  great  blessing ;  and  it 
should  be  a  settled  policy  with  this  large  and 
influential  class  of  citizens,  to  encourage  in 
every  possible  way  the  intellectual  cultivation 
of  all  who  compose  their  body. 

The  kind  of  education  which  is  suitable  for 


APPLICATION  OF  SCIENCE  TO  ART.        33] 

a  mechanic  is  that  which  is  best  accommodated 
to  his  circumstances.  It  should  be  liberal, — 
not  minute.  To  learn  the  practical  application 
of  every  science  to  every  art,  is  not  in  the 
power  of  any  single  individual ;  but  the  me- 
chanic, as  well  as  the  professed  scholar,  may 
learn  the  general  laws  and  principles  of  science; 
and  subsequently  carry  out  to  any  degree  which 
may  seem  expedient  for  him,  those  details  which 
are  particularly  applicable  to  his  own  trade. 
His  general  acquaintance  with  the  physical  laws 
will  enlarge  his  sphere  of  usefulness,  and  in- 
crease his  chances  of  success  in  any  particular 
art. 

There  are  many  good  reasons  why  the  Ame- 
rican mechanics,  more  than  those  of  any  other 
nation,  should  cultivate  science.  One  reason 
of  this  is  the  exalted  station  in  society  which 
he  enjoys  here,  compared  with  that  assigned  to 
the  same  class  of  men  in  other  countries. 

In  this  connexion,  I  will  again  quote  the  au- 
thority of  Governor  Everett. 

And  first,  he  says,  it  is  beyond  all  ques- 
tion, that  what  are  called  the  mechanical  trades 
of  this  country  are  on  a  much  more  liberal 
footing  than  they  are  in  Europe.  This  circum- 
stance not  only  ought  to  encourage  those  who 
20* 


232  THE  YOUNG  MECHANIC. 

pursue  them,  to  take  an  honest  pride  in  im- 
provement, but  it  makes  it  their  incumbent  duty 
to  do  so.  In  almost  every  country  of  Europe, 
various  restraints  are  imposed  on  the  mecha- 
nics, which  almost  amount  to  slavery.  A  good 
deal  of  censure  has  been  lately  thrown  on  the 
journeymen  printers  of  Paris,  for  entering  into 
combinations  not  to  work  for  their  employers, 
and  for  breaking  up  the  power  presses,  which 
were  used  by  the  great  employing  printers.  I 
certainly  shall  not  undertake  to  justify  any  acts 
of  illegal  violence,  and  the  destruction  of  pro- 
perty. But  when  you  consider  that  no  man 
can  be  a  master  printer  in  France  without  a 
license,  and  that  only  eighty  licenses  were 
granted  in  Paris,  it  is  by  no  means  wonderful 
that  the  journeymen,  forbidden  by  law  to  set 
up  for  themselves,  and  prevented  by  the  power 
presses  from  getting  work  from  others,  should 
be  disposed,  after  having  carried  through  one 
revolution  for  the  government,  to  undertake 
another  for  themselves.  Of  what  consequence 
is  it  to  a  man,  forbidden  by  the  law  to  work 
for  his  living,  whether  Charles  X.  or  Louis 
Philip  is  king  ? 

In  England,  it  is  exceedingly  difficult  for  a 
mechanic  to  obtain  a  settlement  in  any  town 


CONDITION  OF  FOREIGN  MECHANICS.      333 

except  that  in  which  he  was  born,  or  where  he 
served  his  apprenticeship.  The  object  of  impos- 
ing these  restrictions  is,  of  course,  to  enforce  on 
each  parish  the  maintenance  of  its  native  poor ; 
and  the  resort  of  mechanics  from  place  to  place 
is  permitted  only  on  conditions  with  which 
many  of  them  are  unable  to  comply.  The  con- 
sequence is,  they  are  obliged  to  stay  where  they 
were  bora ;  where,  perhaps,  there  are  already 
more  hands  than  can  find  work ;  and,  from  the 
decline  of  the  place,  even  the  established  arti- 
sans want  employment.  Chained  to  such  a  spot, 
where  chance  and  necessity  have  bound  him,  the 
young  man  feels  himself  but  half  free.  He  is 
thwarted  in  his  choice  of  a  pursuit  for  life,  and 
obliged  to  take  up  with  an  employment  against 
his  preference,  because  there  is  no  opening  in  any 
other.  He  is  depressed  in  his  own  estimation, 
because  he  finds  himself  unprotected  in  society. 
The  least  evil  likely  to  befall  him  is,  that  he 
drags  along  a  discouraged  and  unproductive 
existence.  He  more  naturally  falls  into  dissi- 
pation and  vice,  or  enlists  in  the  army  or  navy ; 
while  the  place  of  his  nativity  is  gradually  be- 
coming a  decayed,  and  finally  a  rotten  borough, 
and,  as  such,  enables  some  rich  nobleman  to 


234  THE  Y°UNG  MECHANIC. 

send  two  members  to  parliament,  to  make  laws 
against  combinations  of  wcrkmen. 

In  other  countries  singular  institutions  exist, 
imposing  oppressive  burdens  on  the  mechanical 
classes.  1  refer  now  more  particularly  to  the 
corporations,  guilds,  or  crafts,  as  they  are  called, 
that  is,  to  the  companies  formed  by  the  mem- 
bers of  a  particular  trade.  These  exist,  with 
great  privileges,  in  every  part  of  Europe ;  in 
Germany,  there  are  some  features  in  the  insti- 
tution, as  it  seems  to  me,  peculiarly  oppressive. 
The  different  crafts  in  that  country  are  incorr 
porations  recognized  by  law,  governed  by 
usages  of  great  antiquity,  with  funds  to  defray 
the  corporate  expenses,  and  in  each  consider- 
able town,  a  house  of  entertainment  is  selected, 
as  the  house  of  call  (or  harbour,  as  it  is  styled,) 
of  each  particular  craft.  No  one  is  allowed  to 
set  up  as  a  master  workman,  in  any  trade,  un- 
less he  is  admitted  as  a  freeman,  or  member  of 
the  craft;  and  such  is  the  stationary  condition 
of  most  parts  of  Germany,  that  I  understand 
that  no  person  is  admitted  as  a  master  work- 
man in  any  trade,  except  to  supply  the  place 
of  some  one  deceased  or  retired  from  business. 
When  such  a  vacancy  occurs,  all  those  desirous 
of  being  permitted  to  fill  it,  present  a  piece  of 


CONDITION  OF  FOREIGN  MECHANICS. 

work,  which  is  called  their  master-piece,  being 
offered  to  obtain  the  place  of  a  master  work- 
man. Nominally,  the  best  workman  gets  the 
place ;  but  you  will  easily  conceive,  that,  in 
reality,  some  kind  of  favouritism  must  generally 
decide  it.  Thus  is  every  man  obliged  to  sub- 
mit to  all  the  chances  of  a  popular  election, 
whether  he  shall  be  allowed  to  work  for  his 
bread;  and  that  too,  in  a  country  where  the 
people  are  not  permitted  to  have  any  agency  in 
choosing  their  rulers.  But  the  restraints  on 
journeymen,  in  that  country,  are  still  more  op- 
pressive. As  soon  as  the  years  of  apprentice- 
ship have  expired  the  young  mechanic  is 
obliged,  in  the  phrase  of  the  country,  to  wander 
for  three  years.  For  this  purpose  he  is  furnish- 
ed by  the  master  of  the  craft  in  which  he  has 
served  his  apprenticeship,  with  a  duly  authen- 
ticated wandering  book,  with  which  he  goes 
forth  to  seek  employment.  In  whatever  city 
he  arrives,  on  presenting  himself,  with  this  cre- 
dential, at  the  house  of  call,  or  harbour,  of  the 
craft  in  which  he  has  served  his  time,  he  is  al- 
lowed, gratis,  a  day's  food  and  a  night's  lodging. 
If  he  wishes  to  get  employment  in  that  place, 
he  is  assisted  in  procuring  it.  If  he  does  not 


236  THE  YOUNG  MECHANIC. 

wish  to,  or  fails  in  the  attempt,  he  must  pursue 
his  wandering ;  and  this  lasts  for  three  years, 
before  he  can  be  any  where  admitted  as  a  mas- 
ter. I  have  heard  it  argued,  that  this  system 
had  the  advantage  of  circulating  knowledge 
from  place  to  place,  and  imparting  to  the  young 
artisan  the  fruits  of  travel  and  intercourse  with 
the  world.  But  however  beneficial  travelling 
may  be,  when  undertaken  by  those  who  have 
the  capacity  to  profit  by  it,  I  cannot  but  think 
that  to  compel  every  young  man,  who  has  just 
served  out  his  time,  to  leave  his  home,  in  the 
manner  I  have  described,  must  bring  his  habits 
and  morals  into  peril,  and  be  regarded  rathei  as 
a  hardship  than  as  an  advantage.  There  is  no 
sanctuary  of  virtue  like  home. 

You  will  see,  from  these  few  hints,  the  na- 
ture of  some  of  the  restraints  and  oppressions 
to  which  the  mechanical  industry  of  Europe  is 
subjected.  Wherever  governments  and  corpo- 
rations thus  interfere  with  private  industry,  the 
spring  of  personal  enterprise  is  unbent.  Men 
are  depressed  with  a  consciousness  of  living 
under  control.  They  cease  to  feel  a  respon- 
sibility for  themselves,  and,  encountering  ob- 
stacles whenever  they  step  from  the  beaten  path, 
they  give  up  improvement  as  hopeless.  I  neeJ 


CONDITION  OF  FOREIGN  MECHANICS.      £3^ 

Hot  remark  on  the  total  difference  of  things  in 
America.  We  are  apt  to  think,  that  the  only  thing 
in  which  we  have  improved  on  other  countries, 
is  our  political  constitution,  whereby  we  choose 
our  rulers,  instead  of  recognizing  their  heredi- 
tary rights.  But  a  mi  oh  more  important  differ- 
ence between  us  an  !  foreign  countries  is 
wrought  into  the  very  texture  of  our  society ; 
it  is  that  generally  pervading  freedom  from  re- 
straint, in  matters  like  those  I.  have  just  speci- 
fied. In  England,  it  is  said  that  forty  days 
undisturbed  residence  in  a  parish  gives  a  jour- 
neyman mechanic  a  settlement,  and  consequent- 
ly entitles  him,  should  he  need  it,  to  support 
from  the  poor  rates  of  that  parish.  To  obviate 
this  effect,  the  magistrates  are  on  the  alert,  and 
instantly  r  ipel  a  new  comer  from  their  limits, 
who  d'  js  not  possess  means  of  giving  security, 
such  as  few  young  mechanics  command.  A 
duress  like  this,  environing  the  young  man,  on 
his  entering  into  life,  upon  every  side,  and  con- 
demning him  to  imprisonment  for  life  on  the 
spot  where  he  was  born,  converts  the  govern- 
ment of  the  country, — whatever  be  its  name,—- 
into,  a  despotism. 

Such  is  the  condition  of  mechanics  abroad ; 
such,  thanks  to  our  free  institutions  and  the 


238 


THE  YOUNG  MECHANIC. 


bounty  of  a  good  Providence,  is  not  the  condi- 
tion of  mechanics  here.  They  may — in  fact 
they  must  neglect  the  cultivation  of  their 
minds ;  but  the  American  mechanic  is  inexcus- 
able if  he  neglects  the  great  privileges  Avhich 
distinguish  him  from  the  less  fortunate  Euro- 
pean. 

Another  reason  why  the  American  mechanic 
should  cultivate  his  intellectual  powers  as  far 
as  possible,  is  the  vastly  wider  field  which  is 
opened  to  him  by  the  extent  and  the  resources 
of  his  country,  and  the  ever  active  enterprize 
of  its  citizens.  The  European  mechanic  is 
hedged  in  on  every  side  by  restriction,  and  by 
competitors  without  number.  All  the  trades 
there  are  full.  In  our  country  we  see  the  re- 
verse. Here  we  have  not  men  enou  ^h  to  per- 
form the  work  required.  The  demand  for  me- 
chanical industry  has  never  been  fully  met,  and 
cannot  be,  for  a  long  time  to  come.  The  im- 
mense amount  of  our  land,  the  preponderance 
of  agricultural  industry,  and  the  increasing  de- 
mands of  commerce,  open  an  unlimited  field  to 
mechanical  enterprise.  We  may  infer  what 
may  yet  be  done  from  what  has  already  been 
done.  The  service  which  the  mechanical  in- 
genuity of  Americans  has  already  rendered  to 


TRIUMPHS  OF  AMERICAN  INGENUITY.      239 

.ihe  country  is  at  once  a  source  of  pride  and  .of 
hope.  Take,  for  example,  the  service  rendered 
to  the  cotton  growing  interest  by  Whitney's 
invention  of  the  saw-gin ;  or  that  rendered  to 
internal  commerce  and  to  agriculture  by  Ful- 
ton's introduction  of  the  steamboat  into  general 
use ;  or  that  rendered  to  every  consumer  in  the 
country  by  inventors  and  manufacturers  con- 
cerned in  the  production  of  cotton  and  woollen 
fabrics.  These  inventions  and  improvements, 
by  increasing  the  resources  of  the  country, 'have 
greatly  increased  the  demand  for  mechanical 
products.  Whether,  therefore,  the  American 
mechanic  addresses  himself  to  increasing  the 
quantity  or  improving  the  quality  of  his  manu- 
iactures,  the  field  before  him  is  wide  enough 
for  his  greatest  powers  and  his  most  unwearied 
activity.  In  entering  upon  this  field,  let  him 
remember  that  knowledge  is  power,  and  he 
will  neglect  no  opportunity  of  impr  ing  his 
mind. 


21 


240  THE  YOUNG  MECHANIC 


CHAPTER  VII. 

MEANS   OF  INTELLECTUAL   CULTIVATION 
ACCESSIBLE  TO  THE  MECHANIC. 

SUPPOSING  that  the  reasons  why  an  American 
mechanic  should  be  well  educated  are  suffi- 
ciently established,  let  us  next  consider  the 
means  which  are  at  his  disposal  or  may  be 
brought  within  his  reach. 

1.  Of  course  the  first  and  most  important 
means  of  intellectual  cultivation  are  the  schools ; 
and  those  to  the  improvement  of  which  the 
efforts  of  mechanics  as  a  body  can  be  most 
serviceably  directed  are  the  public  schools. 
Wherever  a  system  of  public  schools  exists,  it 
is  the  interest  of  the  mechanic,  in  common 
with  all  other  citizens,  to  aid  in  rendering  it  as 
perfect  as  possible.  I  believe  that  it  is  essen- 
tial to  the  perfection  of  a  system  of  public 
schools,  that  not  only  elementary  instruction 
should  be  dispensed  to  the  children  of  all  citi- 
zens who  require  it ;  but  that  schools  of  a 
higher  order  should  be  placed  within  the  reach 
of  all  pupils  whose  parents  may  wish  to  obtain 


SCHOOLS. 


the  advantages  of  higher  instruction  for  their 
offspring.  Experience  shows  that  it  is  not  a 
difficult  matter  to  create  a  supply  of  this  highei 
instruction  equal  to  the  demand,  even  where 
the  provision  of  primary  instruction  is  most 
abundant.  In  Boston,  where  the  population  is 
over  eighty  thousand,  and  the  primary  and 
grammar  schools  are  sufficient  to  accommodate 
every  applicant  for  admission  without  delay, 
the  High  School  for  twenty  years  has  averaged 
only  ninety  pupils  ;  this  being  the  whole  num 
ber  of  qualified  candidates  offered  for  admis 
sion. 

In  Philadelphia  the  supply  has  certainly  been 
hitherto  equal  to  the  demand,  as  all  applicants 
for  admission  to  the  High  School  who  were 
qualified  for  the  higher  studies  at  the  time  of 
their  examination  have  been  admitted.  I  be 
lieve  that  the  number  of  scholars  who  will 
leave  the  school  every  year  to  enter  upon  the 
active  business  of  life,  will  always  be  found 
equal  to  those  who  shall  be  qualified  for  admis- 
sion and  shall  present  themselves  for  exami- 
nation. The  advantages  resulting  from  High 
Schools  are  not  confined  to  the  pupils  who  re- 
ceive instruction  at  those  schools.  The  stimu- 
lus afforded  by  the  hope  of  attaining  admission 


242  TIIE  YOUNG  MECHANIC. 

to  them  arts  upon  all  the  other  schools,  pro- 
ducing greater  exertion  and  a  more  rapid  pro- 
gress in  learning.  In  fact  the  whole  system  is 
not  only  improved,  but  greatly  extended,  by 
the  existence  of  higher  classes  of  schools, 
This  is  apparent  in  this  city,*  where  a  greater 
number  of  primary  and  grammar  schools  have 
been  created  since  the  erection  of  the  High 
School  than  at  any  previous  period  of  the  same 
length.  The  High  School  flinches  to  the 
future  mechanic  precisely  the  liberal  kind  of 
instruction  which  will  be  most  available  to  him 
in  his  trade ;  and  in  some  instances  gives  mi- 
nute practical  information  directly  applicable  to 
the  arts ;  as  for  example,  in  the  mathematical  and 
drawing  lessons,  and  the  lessons,  lectures  and 
experiments  on  chemistry,  natural  philosophy 
and  natural  history  ;  other  parts  of  the  course  of 
instruction,  as  the  training  in  logic,  rhetoric 
a.id  composition,  have  more  direct  reference  to 
the  pupil's  future  position  in  the  community  as  a 
citizen,  a  public  officer,  a  parent,  or  a  teacher. 
Such  institutions  it  is  the  interest  of  every  man 
to  sustain ;  of  the  rich,  who  do  not  avail  them- 
selves of  this  advantage  for  their  own  children, 

*  Philadelphia. 


MECHANICS'  INSTITUTES. 

equally  with  those  who  are  not  rich,  and  there- 
fore need  their  aid.  In  fact,  the  laws  which  dis- 
tribute property  equally  among  heirs,  render  it 
probable  that  the  grand-children,  or  great-grand- 
children of  the  richest  man  in  any  of  our  com- 
munities will  become  pupils  in  the  public 
schools.  Jt  is,  therefore,  the  rich  man's  in- 
terest  to  pay  heavy  taxes,  if  need  be,  in  ordei 
that  the  public  schools  may  be  rendered  perfect, 
2.  The  inheritance  which  he  will  thus  trans- 
mit to  his  posterity,  will  last  long  after  his 
wealth  shall  have  been  scattered  to  the  winds 
I  pass  with  reluctance  from  this  interesting  part 
of  the  subject,  to  the  next  means  of  intellec- 
tual improvement  for  the  mechanic,  viz. :  the 
Mechanic's  Institute.  Any  youth  who  has 
been  taught  to  read  and  write,  may  derive  ad- 
vantages from  the  lectures,  experiments  and 
library  of  the  Mechanic's  Institute;  and  the 
system  of  operations  in  these  admirable  insti- 
tutions is  so  liberally  expanded,  that  the  most 
accomplished  scholar  may  also  increase  the 
amount  of  his  practical  knowledge  by  having 
recourse  to  the  means  of  improvement  which 
they  afford.  3.  But  the  best  of  all  instruction 
is  self  instruction,  and  the  most  available  means 
which  the  young  man  who  is  determined  to 


244  THE  YOUNG  MECHANIC. 

instruct  himself  can  employ,  are  the  library  and 
the  apparatus  which  are  immediately  at  his  own 
disposal — under  his  own  roof — in  his  own  apart- 
ment. The  great  secret  of  self  improvement 
is  to  dedicate  a  portion  of  every  day  to  private 
study.  Consult  the  biographies  of  a  long  line 
of  self  taught  men  who  have  advanced  science 
and  the  arts  by  their  individual  exertions,  and 
you  will  find  in  most  instances  that  the  bril- 
liant discovery  which  astonished  the  w6rld 
was  the  result  of  private  study  and  unassisted 
experiment.  You  will  find  also  that  the  hour 
redeemed  from  ordinary  business,  and  conse- 
crated to  some  favourite  scientific  inquiry,  was 
the  great  discoverer's  choicest  recreation,  the 
delight  of  the  day,  the  great  reward  of  many 
labours  and  cares.  We  all  have  our  favourite 
enjoyments,  apart  from  our  daily  labour.  While 
one  man  reads  for  recreation,  another  plays 
upon  the  flute  or  takes  a  ride,  or  sketches  a 
landscape,  or  talks  politics,  or  tells  stories  to 
his  children.  All  these  amusements  are  excel- 
lent and  refreshing  in  their  season — all  are 
looked  -forward  to  with  pleasure ;  but  a  sweeter 
recreation  than  any  of  these  awaits  the  man 
who  is  at  once  a  hard  worker  and  a  devotee  of 
science.  Often  in  the  course  of  a  busy  day  do 


MECHANICS'  INSTITUTES.  245 

his  thoughts  bound  forward  to  the  happy  mo- 
ment when  he  shall  enter  the  sanctuary  of  his 
own  study,  leaving  his  toils  and  cares  behind, 
and,  "  the  world  forgetting,  by  the  world  for- 
got," shall  busy  himself  in  his  favourite  pur- 
suits, studying,  experimenting,  calculating,  till 
his  brain  is  weary  with  pleasurable  excitement, 
and  tired  nature  claims  the  right  of  repose.  Jn 
order  to  profit  by  study  it  is  not  absolutely  ne- 
cessary, but  it  is  certainly  very  convenient  and 
agreeable  to  have  a  place,  a  room,  be  it  ever  so 
small  or  so  poorly  furnished,  which  the  stu- 
dent, the  self  instructer,  may  call  his  own — his 
castle — his  sanctuary.  Here  he  treasures  up 
his  little  library  of  books,  few  perhaps,  but 
choice  and  well  beloved.  Here  he  has  his 
desk,  papers,  and  his  collection  of  curious  or 
useful  things,  each  fraught  with  associations, 
each  the  occasion  of  a  lesson  to  himself.  The 
mineral,  which  is  but  a  common  pebble  to  the 
visitor  who  comes  in  to  look  at  his  cabinet,  has  a 
magic  power  in  it  for  the  collector  himself.  It 
brings  back  to  his  recollection  the  glorious 
mountain  towering  to  the  skies — the  cataract — 
the  deep  cavern,  or  the  broad  prairie,  where  the 
wonderful  gem  was  found — wonderful  by  the 
power  of  association  which  it  has  over  the  mind 


YOUNG  MECHANIC. 


of  its  finder.  The  well  worn  volume,  which  ia 
mere  paper  and  print  to  another,  is  a  precious 
treasure  to  him,  who  has  learnt  from  it  the  great 
laws  of  nature,  the  lore  of  antiquity,  or  the 
sweets  of  poetry.  Every  article  in  this  retreat 
of  studious  leisure  has  a  value  to  the  owner,  as 
it  is  connected  with  the  developement  of  his 
higher  faculties.  -  Every  article  is  praised  for 
having  been,  in  its  turn,  the  instrument  of  self 
cultivation.  It  would  occupy  too  much  time  to 
enter  here  into  a  detailed  review  of  the  various 
means  of  self  cultivation  to  which  the  student 
may  have  recourse  in  the  retirement  of  his  own 
room.  These  will  form  the  subject  of  a  future 
chapter. 


INTELLECTUAL  CULTIVATION.  247 


CHAPTER  VIII. 

REWARDS    OF    INTELLECTUAL    CULTIVA- 
TION  ACCESSIBLE  TO  THE  MECHANIC. 

I  WILL  now  offer  a  few  remarks  on  thewe- 
wards  of  intellectual  cultivation.  Liberal  know- 
ledge, like  virtue,  is  in  a  certain  sense  its  own 
reward.  The  developement  of  the  intellectual 
powers  is  attended  with  positive  gratification, 
resulting  from  a  sense  of  increased  power,  and 
the  satisfying  of  curiosity  respecting  the  laws 
of  nature.  The  famous  story  of  the  rapture 
of  Archimedes  when  he  arrived  at  his  beautiful 
demonstration  of  a  well  known  mathematical 
truth,  is  but  one  among  a  thousand  proofs  that 
science  rewards  her  votaries  on  the  instant, 
pays  her  workmen,  in  solid  coin,  by  the  day — 
by  the  hour.  This  is  the  sweetest  and  best 
reward  of  intellectual  labour.  It  is  that  which 
is  most  diligently  sought  and  most  highly 
prized. 

But  there  are  other  rewards,  only  incidental 
and  inferior,  but  still  worthy  of  some  conside- 
ration. 


248  THE  YOUNG  MECHANIC. 

1.  Liberal  knowledge  and  accomplishments 
confer  the  advantage  of  an  elevated  and  influ- 
ential position  in  society.  It  is  generally  un- 
derstood that  society  exacts  from  each  of  its 
members  some  price  of  admission  to  its  cote- 
ries and  saloons.  One  brings  fashion,  another 
the  wealth  and  consequence  of  his  family, 
another  his  musical  or  conversational  talents, 
another  his  celebrity  as  an  author  or  traveller, 
or  distinguished  stranger.  Among  the  rest  the 
votary  of  science  prefers  his  claim,  and  finding 
it  admitted,  takes  a  place  in  society  on  an  inde- 
pendent and  respectable  ground.  He  is  ad- 
mitted for  what  he  is,  not  for  what  he  has,  or 
what  his  ancestors  had. 

2.  Again,  liberal  knowledge  gives  its  posses- 
sor the  means  of  enjoyment  in  sickness,  in 
retirement,  and  in  old  age.  He  who  has  learnt 
to  converse  with  the  master  spirits  of  other 
times,  is  never  at  a  loss  for  society  or  amuse- 
ment. Give  him  a  book  and  he  is  happy — or, 
failing  the  book,  his  previous  cultivation  makes 
the  communion  of  his  own  thoughts  or  the 
practice  of  composition  a  sufficient  occupation 
to  pass  delightfully  those  hours  of  loneliness 
and  silence  which  are  a  weariness  to  the  illite- 
rate man. 


INTELLECTUAL  CULTIVATION.  £49 

3.  To  the  advantages  which  the  scientific 
mechanic  enjoys  in  the  prosecution  of  his  trade 
we  have  already  adverted.  We  will  name  but 
one  more  before  closing  the  present  considera- 
tion of  the  subject.  It  is  this  : — The  members 
of  any  particular  trade,  by  earnestly  uniting  in 
the  use  of  the  various  means  of  intellectual 
cultivation  within  their  reach,  may  greatly  in- 
crease the  respectability,  wealth  and  influence 
of  that  trade.  By  possessing  their  own  library, 
reading  room,  museum  and  apparatus,  and  by 
stimulating  the  exertions  of  every  member  of 
the  trade,  master,  journeyman,  and  apprentice, 
they  will  soon  come  to  be  recognised  as  a 
scientific  body;  and  will  not  only  insure  to 
themselves  the  other  rewards  of  science,  but 
will  receive  the  grateful  acknowledgments  of 
their  fellow  citizens  as  public  benefactors. 

Such  are  the  rewards  of  intellectual  cultiva- 
tion attainable  by  those  who  are  engaged  in  the 
mechanical  trades.  The  example  of  Franklin, 
Watt,  Arkwright,  and  a  host  of  other  illustrious 
men,  show  what  mechanics  have  done.  It  re- 
mains for  the  rising  generation  in  our  own 
happy  land  to  show  what  mechanics  can  do. 


250  THE  YOUNG  MECHANIC 

CHAPTER  DC 
THE  MECHANIC'S  STUDIES] 

BOOKS  are,  generally  speaking,-too  volumin- 
ous ;  writers  descend  too  much  into  minutiae ; 
and  it  is  ?.n  old  observation,  that  where  men 
are  determined  t°>  write  every  thing  which  can 
be  said  an  any  subject,  they  may  write  to 
eternity.  Hence  it  is  that  a  man  of  sense  and 
erudition  need  but  open  a  sf "ogle  page  of  many 
a  modern  volume  to  lay  it  aside  forever.  It  is 
said  of  Didymus,  an  ancient  gramrrii^ian,  that 
he  had  written  so  much  that  lie  knew  not  his 
own  productions,  and  having  once  abused  a 
work  for  its  absurdity,  it  was  found  to  be  his 
owri.  I  fear  the  race  of  Didymus  is  not  extinct.* 

To  read  all  books  on  all  subjects  would  re- 
quire an  uninterrupted  attention  during  the 
longest  life,  even  of  an  antediluvian.  To  read 
only  the  most  celebrated,  written  in  a  few  lan- 
guages, is  an  employment  sufficient  to  fill  up 
every  hour  of  laborious  application.  For  the 

*  Northraore. 


CHOICE  OF  BOOKS.  £5 

fiake  then  of  saving  time,  and  of  directing  the 
judgment  of  the  inexperienced,  it  becomes  an 
useful  attempt  to  suggest  some  general  hints, 
which  may  tend  to  facilitate  selection.  One 
rule  of  the  greatest  consequence  is,  to  read 
only,  or  chiefly,  the  original  treatises  in  all  the 
various  departments  of  science  or  of  literature. 
Nearly  the  same  space  of  time,  though  not  the 
same  degree  of  attention,  is  necessary  to  peruse 
the  faint  copies  of  imitative  industry,  as  would 
appropriate  to  the  student  the  solid  productions 
of  native  genius.  This  rule  is  more  particu- 
larly to  be  observed  on  the  first  entrance  on 
smdy.  The  foundation  must  be  laid  deeply, 
and  formed  of  solid  materials.  The  superstruc- 
ture will  often  admit  slight  and  superficial  ap- 
pendages. When  we  have  studied  the  fine 
relics  of  those  who  have  lived  before  us,  we 
may  derive  much  pleasure  from  attending  to 
the  additional  labours  of  contemporary  genius. 
But  to  begin  with  these  is  to  found,  like  the 
fool  recorded  in  the  gospel,  an  edifice  in  the 
sand.* 

The  merit  of  a  book  consists  in,   1,  New 
facts  j  2.  JN  ew  inferences  from  established  facts ; 


*  Ivnox's  Essays. 

22 


252  THE  YOUNG  MECHAN  C. 

3.  A  better  arrangement ;  4.  A  more  complete 
collection  of  facts ;  5.  information.  When  a 
book  is  destitute  of  these  requisites,  it  may  be 
condemned,  without  mercy,  as  of  no  use  what- 
ever, and  immediately  sold  by  weight  to  the 
cheesemonger,  or  consigned  to  any  other  base 
or  more  ignoble  purpose.  When  it  is  not  des- 
titute of  these,  it  should  be  reprieved,  acquitted, 
or  applauded,  according  to  the  requisites  which 
it  possesses.* 

On  the  choice  of  books,  most  excellent  ad- 
vice is  given  by  Dr.  Watts,  from  whom,  and 
other  authors,  has  been  compiled  a  pocket 
volume  "  on  the  Improvement  of  the  Mind," 
in  which  various  interesting  matter  relating  to 
books,  reading,  conversation,  study,  &c.  are 
treated  of.  Happy  are  they,  says  Fenelon, 
who  being  disgusted  with  all  violent  pleasures, 
know  how  to  content  themselves  with  the 
swaets  of  an  innocent  life.  Happy  are  they, 
who  are  diverted,  at  the  same  time  that  they 
are  instructed,  and  please  themselves  by  en 
riching  their  minds  with  knowledge.  Where- 
ever  they  may  be  thrown  by  adverse  fortune, 
they  will  carry  their  own  entertaii  ment  with 

*  Dr.  Mosley. 


CHOICE  OF  BOOKS.  253 

them ;  and  the  uneasiness,  which  preys  on 
others,  even  in  the  midst  of  their  pleasures,  is 
unknown  to  those  who  can  employ  themselves 
in  reading.  Happy  are  they  who  love  books 
and  are  not  deprived  of  them. 

Among  the  other  improvements  of  the  pre- 
sent age,  the  art  of  puffing  appears  to  have 
arrived  at  such  perfection  that  it  is  impossible 
to  select  books  by  their  titles,  or  from  some  of 
our  booksellers'  account  of  them  in  their  ad- 
vertisements. A  person  who  would  make  a 
preference  and  choose  the  best,  must  read  much 
beyond  the  title  page.  From  a  hand  bill  which 
accidentally  lies  on  the  compiler's  desk,  the 
following  encomiums  are  bestowed  on  very 
immethodical  and  inferior  works.  u  A  fasci 
nating  introduction,  superior  to  every  preceding 
attempt  of  the  kind,  and  deserving  of  universal 
preference."  "  The  most  approved  and  gene- 
rally adopted  book  ever  published,  and  un- 
doubtedly the  best  extant."  Such  parade  of 
applause  may  pass  with  those  who  do  riot 
compare  and  discriminate,  and  their  number  is 
unfortunately  not  small. 

Mr.  Pratt  ingeniously  laments  the  strange 
circumstance,  that  authors  themselves  have 
been  the  most  bitter  detractors  of  the  talents 


254  THE  YOUNG  MECHAN/C. 

and  reputations  or  each  othei.  A  grievance 
far  more  disgraceful,  if  not  more  injurious,  to 
the  literaiy  chaiacter,  than  any  other  species 
of  criticism.  Indeed  it  would  be  difficult  to 
find  any  set  of  enemies  among  men,  any  per- 
sons, whose  passions  and  interests  are  at  va- 
riance, so  full  of  acerbity,  of  open  violence,  or 
of  concealed  malice,  as  the  most  eminent  writers 
have  proved  themselves  to  each  other,  in  their 
contentions  of  rivalry.  The  u  republic  of  let- 
ters" is  a  very  common  expression  among  Eu- 
ropeans, and  yet,  when  applied  to  the  learned 
of  Europe,  is  the  most  absurd  which  can  be 
imagined,  since  nothing  is  more  unlike  a  repub- 
lic, than  the  society  which  goes  by  that  name 
In  truth,  almost  every  member  of  this  fancied 
commonwealth  is  desirous  of  governing,  and 
none  willing  to  obey :  each  looks  upon  his 
fellow  as  a  rival,  not  an  assistant  in  the  same 
pursuit.  They  calumniate,  they  injure,  they 
despise,  they  riuicule,  they  worry,  and  assas- 
sinate each  other.  If  one  man  write  a  book 
which  pleases,  others  write  books  to  show  thai 
he  might  have  given  still  greater  pleasure,  or 
should  not  have  attempted  to  please.  If  one 
happen  to  hit  upon  something  new,  numbers 
are  ready  to  assure  the  public  that  all  this  was 


CHOICE  OF  BOOKS.  255 

no  novelty  to  them  or  the  learned ;  that  Car- 
danus,  or  Brunus,  or  some  other  author,  too 
dull  to  be  generally  read,  had  anticipated  the 
discovery.  Their  jarring  constitution,  instead 
of  being  styled  the  republic  of  letters,  should 
be  entitled  the  anarchy  of  literature.  It  is  true, 
there  are  some  of  superior  abilities,  who  reve- 
rence and  esteem  each  other ;  but  their  mutual 
admiration  is  not  sufficient  to  shield  off  the 
contempt  of  the  crowd.  The  wise  are  but 
few,  and  they  praise  with  a  feeble  voice ;  the 
vulgar  many,  and  roar  in  reproaches.  The 
trnly  grrat  seldom  unite  in  societies,  have  few 
meetings,  and  no  cabals :  the  dunces  hunt  in 
full  cry,  till  they  have  run  down  a  reputation, 
and  then  snarl  and  fight  with  each  other  about 
dividing  the  spoil."  No  task  would  be  more 
easy  to  the  most  superficial  observer,  than  that 
of  producing  numerous  instances  of  glaring 
partiality  in  the  journals  of  several  of  our  cri- 
tics by  profession.  It  appears  sometimes  from 
their  neglect  in  reading  with  care  the  book 
which  they  undertake  to  criticize,  so  as  to 
comprehend  the  author's  views ;  sometimes  the 
narrowness  of  party  spirit  warps  their  decisions, 
in  open  contempt  of  the  power  of  genius  and 
originality.  Sometimes  a  publisher's  name  on 
22* 


256  THE  YOUNG  MECHANIC. 

the  cover,  connected  with  the  imprint  of  the 
book,  is  a  clue  by  which  neglect,  injustice, 
narrow-minded  selfishness,  and  misrepresenta- 
tion, may  be  unravelled ;  and  sometimes  the 
critic's  private  jjique,  as  a  contemporary  author, 
is  obvious. 

Poetic  compositions,  whether  in  ancient  or 
modern  languages,  may  be  read  at  vacant  hours, 
with  some  advantage,  because  many  passages 
contain  practical  rules  relating  to  moral  econo- 
my and  religion.  Many  elegant  and  ingenious 
sentiments  and  descriptions  may  also  be  found 
among  the  writings  of  poets,  well  worth  com- 
mitting to  memory ;  and  the  measure  of  verse 
greatly  assists  recollection. 

The  mere  art  of  rhetoric  never  yet  formed 
an  English  orator.  It  is  one  of  those  artificial 
assistances  of  genius,  which  genius  wants  not, 
and  of  which  dullness  can  little  avail  itself. 
But  as  excellent  books  have  been  written  on 
this  subject,  the  general  scholar  will  not  fdil 
to  pay  it  some  attention.  Let  him  then  read 
Cicero  on  the  Orator,  and  Quintilian's  Insti- 
tutes, and  he  need  not  trouble  himself  with 
those  meagre  treatises  which  give  a  hard  name 
to  natural  modes  of  expression,  and  teach  us 
that,  like  Hudibras,  we  cannot  open  our  mouths, 


ELOCUTION  AND  RHETORIC.  257 

but  out  there  flies  a  trope.*  So  much  of  rheto- 
ric as  teaches  the  art  of  speaking  and  writing 
with  elegance  and  dignity,  in  order  to  instruct, 
persuade  and  please,  is  certainly  most  valuable. 
Grammar  teaches  only  propriety  ;  but  rhetoric 
raises  upon  it  purity  and  clearness  of  language, 
elegant  thoughts,  variety  of  expression,  and 
lively  figures.  The  duty  of  the  orator  is  to 
stat3  interesting  truths  with  such  probability 
and  evidence  as  may  gain  belief,  and  with  such 
force  and  simplicity  as  may  produce  conviction. 
He  must  be  able  to  demonstrate,  to  delight,  and 
to  work  on  the  passions. 

Probably  nothing  has  contributed  more  to 
generate  apposite  habits  of  mind  than  the  early 
taste  for  reading.  Books  gratify  and  excite  our 
curiosity  in  innumerable  ways.  They  force  us 
to  reflect.  They  hurry  us  from  point  to  point. 
They  present  direct  ideas  of  various  kinds,  and 
they  suggest  indirect  ones.  In  a  well  written 
book  we  are  presented  with  the  maturest  re-< 
flections,  or  the  happiest  flights,  of  a  mind  of 
uncommon  excellence.  It  is  impossible  tha< 
we  can  be  much  accustomed  to  such  compa- 
Sj  without  attaining  some  resemblance  oi 


Dr. 


258  THE  YOUNG  MECHANIC. 

them.  He  who  revels  in  a  well  chosen  library, 
has  innumerable  dishes,  and  all  of  admirable 
flavour.  His  taste  is  rendered  so  acute,  as  to 
distinguish  the  nicest  shades  of  difference.  His 
mind  becomes  ductile,  susceptible  to  every  im- 
pression, and  gains  new  refinement  from  each. 
His  varieties  of  thinking  baffle  calculation,  and 
his  powers,  whether  of  reason  or  imagination, 
become  eminently  vigorous.*  - 

Exclusive  of  all  regard  to  interest,  and  of 
preparation  for  the  exercise  of  any  art  or  pro- 
fession, says  Dr.  Knox,  a  taste  for  pleasing 
books  is  surely  eligible,  if  it  were  only  for  the 
sake  of  enabling  an  ingenious  man  to  pass  his 
days  innocently,  calmly,  and  pleasurably.  The 
pleasures  of  letters  are  certainly  great  to  those 
who  have  been  early  devoted  to  them,  and  they 
are  of  all  others  the  easiest  to  be  obtained. 
For  with  respect  to  books  we  may  say,  u  These 
are  friends,  no  one  of  whom  ever  denies  him- 
self to  him.  who  calls ;  no  one  takes  leave  of 
his  visitor  till  he  has  rendered  him  happier  and 
more  pleased  with  himself.  The  conversation 
of  no  one  of  these  is  dangerous,  neither  is  the 
respect  to  be  paid  to  him  attended  with  expense. 

*  Godwin's  Enquirer. 


ON  A  TASTE  FOR  READING.  £5^ 

You  may  take  what  you  please  from  them. 
What  happiness,  what  a  glorious  old  age  awaits 
him  who  is  placed  under  the  protection  of  such 
friends  !  He  will  have  those  whom  he  may  con- 
sult on  the  most  important,  and  the  most  trifling 
matter,  whose  advice  he  may  daily  ask  concern- 
ing himself;  from  whom  he  may  hear  the  truth 
without  insult,  praise  without  adulation,  and  to 
whose  similitude  he  may  conform  himself."* 

As  soon  as  we  have  obtained,  by  reading,  a 
competent  knowledge  of  a  book  or  particular 
subject,  it  will  contribute"  greatly  to  animate  us 
in  proceeding  still  farther,  if  we  talk  of  it  either 
with  our  equals  in  attainments,  or  with  the 
learned  and  experienced.  In  such  conversation 
we  venture  to  advance  an  opinion;  our  self- 
love  renders  us  solicitous  to  maintain  it,  we 
seek  the  book  as  an  auxiliary,  we  therefore 
read  it  with  eager  attention.  In  this  manner 
an  attachment  to  books  and  literary  employ- 
ments is  gradually  formed,  and  what  began  in 
labour  or  necessity,  becomes  a  choice,  and  con- 
stitutes the  most  agreeable  pleasure. 

There  is  no  study  so  dry,  but  by  fixing  oui 
attention  upon  it,  we  may  at  last  n*~id  it  capa« 

•v»:  £,    *  Seneca. 


260  THE  YOUNG  MECHANIC 

tfle  of  affording  great  delight.  Metaphysics 
and  mathematics,  even  in  their  abstrusest  parts, 
are  known  to  give  the  attentive  student  a  very 
exalted  satisfaction.  Those  parts,  then,  of  hu- 
man learning,  which  in  their  nature  are  more 
entertaining,  cannot  fail  of  being  beloved  in  a 
high  degree,  when  the  mind  is  closely  and  con- 
stantly applied  to  them. 

In  order  to  acquire  the  power  and  habit  of 
fixing  the  attention,  it  will  be  first  necessary  to 
summon  a  very  considerable  degree  of  resolu- 
tion. In  beginning  the  study  of  a  new  language, 
or  any  book  of  science,  which  presents  ideas 
totally  strange,  the  mind  cannot  but  feel  some 
degree  of  reluctance  or  disgust  But  let  the 
student  persevere;  and  in  a  very  short  time 
the  disgust  will  vanish,  and  he  will  be  reward- 
ed with  entertainment.  Till  this  takes  place, 
let  him  make  it  an  inviolable  rule,  however 
disagreeable,  to  read  a  certain  quantity,  or  for  a 
certain  time,  and  he  will  infallibly  find,  that 
what  he  entered  upon  as  a  task,  he  will  conti- 
nue as  his  best  amusement. 

A  due  degree  of  variety  will  contribute  great- 
ly to  render  reading  agreeable.  For  though 
it  be  true  that  not  more  than  one  or  two  books 
should  be  read  at  once ;  yet,  when  finished,  it 


ON  A  TASTE  FOR  READING.  26 \ 

will  be  proper,  if  any  weariness  be  felt,  to  take 
up  an  author  who  writes  in  a  different  style,  or 
on  a  different  subject;  to  change  from  poetry 
to  prose,  and  from  prose  to  poetry ;  to  inter- 
mix the  moderns  with  the  ancients  ;  alternately 
to  lay  down  the  book  and  take  up  the  pen ;  and 
sometimes  to  lay  them  both  down,  and  enter 
with  alacrity  into  agreeable  company  and  pub- 
lic diversions.  The  mind,  after  a  little  cessa- 
tion, returns  to  books  with  all  the  voracious 
eagerness  of  a  literary  hunger.  But  the  inter- 
missions must  not  be  long,  or  frequent  enough 
to  form  a  habit  of  idleness  or  dissipation. 

The  morning  has  been  universally  approved 
as  the  best  time  for  study ;,  but  at  all  hours  and 
in  all  seasons,  if  we  can  restrain  the  licentious 
rovings  of  imagination ;  soothe  the  passion 
of  the  heart,  and  command  our  attention,  so  as 
to  concentre  it  on  the  subject  we  examine,  we 
shall  find  it  amply  rewarded.  Attend  closely; 
and  close  attention  to  any  worthy  subject  will 
always  prove  solid  satisfaction.  But  particu- 
larly in  reading  it  may  be  depended  on  as  ap- 
proved truth,  that  the  degree  of  profit  as  well 
as  pleasure,  derived  from  it,  will  ever  be  pro- 
portioned to  the  degree  of  attention.* 

*  Kmx's  Essays,  No.  82. 


252  T1IE  Y°UNG  MECHANIC. 

There  are  some  mechanic  aids  in  reading, 
which  may  prove  of  great  utility.  Montaigne 
placed  at  the  end  of  the  book  which  he  intend- 
ed not  to  reperuse,  the  time  he  had  read  it, 
with  a  concise  decision  on  its  merits.  He  has 
obliged  his  admirers  with  giving  several  of  these 
annotations.  The  striking  passages  in  a  book 
may  be  noted  on  a  blank  leaf,  and  the  pages1 
referred  to  with  a  word  of  criticism.  Seneca, 
in  sending  some  volumes  to  his  friend  Lucilius, 
accompanied  them  with  notes  on  particular 
passages,  that,  as  he  observes,  you  who  only 
aim  at  the  useful,  may  be  spared  the  trouble  of 
examining  them  entirely.  I  have  seen  books 
noted  by  Voltaire  with  a  word  of  censure  or 
approbation  on  the  page  itself,  which  was  his 
usual  practice ;  and  these  volumes  are  precious 
to  every  man  of  taste.* 

I  would  have  qyery  one  try  to  form  an 
opinion  of  an  author  himself,  though  mo- 
desty may  restrain  him  from  mentioning  it. 
Many  are  so  anxious  to  have  the  reputation  of 
taste,  that  they  only  praise  the  authors  whose 
merit  is  indisputable.  I  am  weary  of  hearing 
of  the  sublimity  of  Milton,  the  elegance  and 

*  D'Israeli's  Miscellanies. 


ON  A  TASTE  FOR  READING.  263 

harmony  of  Pope,  and  of  the  original,  untaught 
genius  of  Shakspeare.  Such  hackneyed  re- 
marks are  made  by  those  who  know  nothing 
of  nature,  and  can  neither  enter  into  the  spirit 
of  those  authors,  nor  understand  them.* 

Temperance  in  eating  and  drinking,  will  con- 
tribute more  to  improve  the  natural,  force  or 
abilities  of  the  mind,  than  any  art  or  any  ap- 
plication. It  is  related  of  the  unfortunate  young 
Chatterton,  that  he  was  remarkably  abstemious, 
and  that  it  was  a  frequent  and  favourite  maxim 
with  him,  that  a  man  might  arrive  at  any  height 
of  improvf  ment,  or  effect  the  most  arduous  un- 
dertaking by  dint  of  industry  and  abstinence. 
He  practised  what  he  thought ;  and  this  in  some 
degree  accounts  for  his  uncommon  attainments 
and  productions,  at  an  age  when  the  full-fed 
heir  can  scarcely  read  and  write.  I  recommend 
to  all  students  the  perusal  of  Dr.  Cheney's 
Medical  Advice ;  or  I  will  give  it  to  them  in  a 
few  words.  "Take  the  least  and  the  lightest 
food,  under  which  you  can  be  easy."  Your 
80^1  will  thux  feel  fresh  vigour,  your  life  will 
be  longer  and  happier,  and  your  conduct  wiser/f 
The  neglect  of  writing  in  early  life  is  the 


'  Mary  Wollstonecraft.  f  Dr.  Knox. 

23 


2(34  TI1E  Y°UNG  MECHANIC. 

reason  that  almost  every  line  of  our  scholars 
and  gentry  (who  seem  to  pride  themselves  in 
their  bad  penmanship)  stands  in  need  of  an  in- 
terpreter. As  this  art  is  purely  mechanical,  and 
perfected  by  practice  only,  it  is  foreign  from 
my  purpose  to  prescribe  rules  for  its  attain 
ment.  I  will  venture  however  to  assert,  that  a 
plain,  upright  hand,  resembling  the  round  ro- 
man  print  is  preferable  to  the  ridiculous  flour- 
ishes and  slopes  of  writing-masters ;  and  my 
opinion  is  founded  on  a  very  simple  reason,  i* 
is  more  legible.* 

Plain  writing,  says  Dr.  Gregory,  clear  of 
flourishes,  and  very  upright,  is  certainly  the 
most  proper  for  every  station  of  life,  and  will 
remain  intelligible  longer  than  any  other.  It 
may  be  learned  with  less  time  and  trouble,  and 
may  be  written  more  expeditiously.^  I  have 
long  been  of  this  opinion,  and  was  happy  to 
find  it  countenanced  by  the  authority  of  Dr. 
Knox,  and  Dr.  Beattie.  Their  popularity  may 
perhaps  be  of  weight  in  correcting  the  whimsi- 
cal and  unintelligible  mode  of  writing,  which 
has  been  introduced  by  ignorant  schoolmasters 
I  perfectly  agree  with  the  latter,  that  the  writing 

'Yorke. 


ON  THE  ART  OF  WRITING.  265 

which  approaches  nearest  the  Roman  printed 
character,  is  the  completest.  Pope  was  taught 
to  write  by  imitating  and  copying  the  Roman 
character  of  printed  books,  in  which  kind  of 
writing  he  always  excelled.  [The  Italic  printed 
character  appears  better  adapted  for  the  purpose 
of  writing  than  the  Roman.]  A  gentleman  in- 
form H,  by  letter,  his  country  friend  in  Lin- 
colnshire, who  had  done  him  some  recent  fa- 
vour, how  much  he  was  obliged,  and  that  he 
should  soon  send  him  an  equivalent.  Not  being 
accustomed  to  fashionable  scrawls,  he  read  it 
that  his  friend  would  send  him  an  elephant , 
and,  building  a  barn  at  the  time,  actually  fitted 
up  a  stall  for  the  reception  of  his  expected  pre- 
sent. The  arrival,  however,  of  a  barrel  of 
oysters,  a  few  days  afterwards,  helped  him  to 
the  right  reading,  by'  putting  him  in  possession 
of  a  more  suitable  equivalent  than  an  elephant, 
This  is  a  fact,  and  occurred  a  few  years  since.* 

•Rede's  Anecdotes,  1799. 


2(36  THE  YOUNG  MECHANIC 

CHAPTER  X. 
THE  MECHANIC'S  STUDIES. 

To  learn  the  rudiments  of  grammar  by  rote, 
is  not  the  way  to  understand  grammar.  The 
mind  must  be  addressed  and  convinced.  Of 
what  use  is  it  to  vex  a  boy's  memory  with  the 
definition  of  a  noun,  when  the  definition  itself 
is  not  clear  to  his  understanding  ?  We  may  as 
well  show  him  the  figure  of  a  triangle  on  pa- 
per, and  expect  him  to  comprehend  its  nature, 
by  a  definition  of  its  properties.  The  fact  is, 
the  tender  mind  is  not  capable  of  abstract  rea- 
soning; consequently,  every  subject  which  im- 
plies the  generalization  of  ideas,  should  be  first 
unfolded  by  evident  and  palpable  demonstra- 
tion. Thus,  a  boy  is  taught  in  our  schools  to 
gabble  that  u  a  noun  is  the  name  of  any  per- 
son, place,  or  thing,  as  John,  London,  Honour;" 
yet  J  will  venture  to  assert,  that  not  one  in  ten 
thousand  comprehends  what  he  says.  An 
analysis  of  language  was  never  formed,  until 
men  were  enabled  to  observe  the  turns  of 
speech  which  custom  authorizes ;  there  were 


ON  LEARNING  A  LANGUAGE.  267 

poets  and  orators  before  a  grammar  was  ever 
thought  of;  it  would  be  useless  to  teach  either 
By  stems  of  rhetoric  or  composition  to  a  child, 
who  had  not  learnt,  by  frequent  use,  the  proper 
idioms  of  his  own  language ;  and  that  there- 
fore the  best  models  of  beautiful  writing  should 
be  set  before  him,  previous  to  his  being  brought 
to  judge  of  them  by  any  determined  rules.* 

If  grammar  be  taught,  it  must  be  to  one  who 
can  speak  the  language ;  how  else  can  he  be 
taught  the  grammar  of  it?  This  is  evident 
from  the  practice  of  the  wise  and  learned  na- 
tions among  the  ancients.  They  made  it  a  part 
of  education  to  cultivate  their  own,  not  foreign 
tongues.  The  Greeks  counted  all  other  nations 
barbarous,  and  had  a  contempt  for  their  lan- 
guages. And  though  the  Greek  learning  grew 
in  credit  among  the  Romans,  towards  the  end 
of  their  commonwealth,  yet  it  was  the  Roman 
tongue  which  was  made  the  study  of  their 
youth,  It  was  their  own  language  which  they 
were  to  make  <wse  of,  and  therefore  it  was  their 
own  language  they  were  instructed  and  exer- 
cised in. 

But  more  particularly  to  determine  the  pro- 


*  H.  R.  Yorke. 
23* 


268  THE  YOUNG  MECHANIC. 

per  season  for  grammar,  I  do  not  see  how  it 
can  reasonably  be  made  any  one's  study,  but 
as  an  introduction  to  rhetoric.  When  it  is 
thought  time  to  put  any  one  on  the  care  of 
polishing  his  tongue,  and  of  speaking  bettei 
than  the  illiterate,  then  is  the  time  for  him  to 
be  instructed  in  the  rules  of  grammar,  and  not 
before  :  for  grammar  is  designed  not  only  tc 
teach  men  to  speak,  but  to  speak  correctly,  and 
according  to  the  exact  rules  of  the  tongue, 
which  is  one  part  of  elegancy ;  there  is  little 
use  of  the  one  to  him  who  has  no  need  of  the 
other ;  where  rhetoric  is  not  necessary,  gram- 
mar may  be  spared.* 

The  cumbersome  heap  of  worthless  rules 
with  which  grammars  are  crowded,  has  urged 
some  into  the  extreme  of  discarding  them. 
They  have  observed  that  a  quicker  progress 
has  been  made  in  a  language. by  learning  it  by 
mere  rote,  and  from  thence  have  extravagantly 
concluded  that  grammars  are  unnecessary. 
Without  the  assistance  of  the-  rules  of  con- 
struction, it  is  difficult  to  speak  the  living  lan- 
guages well ;  to  say  nothing  of  reducing  sci- 
ence to  principles,  which  contribute  to  form 

*  Locke. 


ON  LEARNING  A  LANGUAGE. 

the  judgment.  But  grammars  ought  to  be  con- 
structed rationally,  whereas  many,  so  far  from 
being  adapted  to  the  capacities  of  children,  sup- 
pose them  to  be  half  philosophers  in  the  outset. 
This  is  evident  from  the  connection  which  the 
rules  have  with  things  with  which  children  are 
unacquainted.* 

With  a  view  of  making  the  study  of  language 
agreeable  and  pleasant,  particularly  to  boys,  it 
is  necessary  that  the  subject  on  which  students 
are  employed  to  read,  be  interesting.  The 
judicious  teacher  can  easily  collect  authors,  in 
almost  every  language,  whose  writings  are  cal- 
culated to  arrest  and  interest  the  mind  at  an 
early  period  of  life.  In  order,  however,  to 
render  the  study  and  comprehension  of  such 
works  easy,  difficult  passages  should  always  be 
satisfactorily  explain^!  in  the  student's  vernacu- 
"lar  tongue,  by  notes ;  and  they  should,  for  be- 
ginners, be  accompanied  with  literal  transla- 
tions.t  + 

Two  things  are  requisite  in  learning  a  lan- 
guage ;  a  knowledge  of  words,  and  skill  in 
putting  them  together  in  writing  or  speaking. 
The  former  is  much  the  more  easy  of  the  two, 

*  De  1'Education  par  M.  de  Crousaz.    f  Dr.  Cowan 


270  THE  YOUNG  MECHANIC 

and  consequently  ought  to  go  first :  to  intermix 
any  foreign  stuff,  as  grammar  with  it,  is  throw- 
ing an  obstacle  in  the  way  of,  boys,  and  hin- 
dering their  progress.  They  are  to  be  kept  to 
but  one  thing  at  a  time,  as  much  as  possible 
To  trouble  them  with  variety,  unless  by  way 
of  refreshing  their  memories,  or  to  prevent  their 
forgetting  what  they  have  already  learnt,  I  think 
a  grand  mistake  in  education,  and  one  main 
occasion  of  that  miserable  work  which  boys 
make  of  it  in  most  schools. 

Though  grammar  be  a  matter  of  importance, 
the  parts  of  language  which  relate  to  the  signi- 
fication of  words,  and  phraseology  are  of 
greater  importanc^e.  In  the  latter  departments, 
a  pupil  cannot  be  overburdened  ;  in  the  former, 
there  are  many  things  not  worth  committing  to 
memory ;  and  he  who  intends  to  make  a  boy  a 
critic  in  grammar,  will  unavoidably  leave  him* 
deficient  in  other  more 'necessary  things.  It 
would  be  the  same  a£if  a  man  should  take 
care  to  let  his  son  be  furnished  with  elegant 
shoes,  while  the  rest  of  his  body  was  clothed 
in  rags.* 

1  very  much  doubt  whether  any  child,  pro- 

*  Clarke's  Essay  on  Education. 


ON  LEARNING  A  LANGUAGE.  211 

digies  excepted,  be  capable  of  learning  two 
languages,  till  it  arrive  at  the  age  of  twelve  or 
thirteen.  1  have  indeed  seen  little  wonderful 
prattlers,  who  were  imagined  to  talk  five  or  six 
different  languages.  I  have  heard  them  suc- 
cessively talk  in  German,  in  Latin,  French,  and 
Italian  words.  They  made  use,  it  is  true,  of 
the  different  terms  of  five  or  six  dictionaries ; 
but  they  spoke  nothing  but  German.  In  a  word, 
fill  a  child's  head  with  as  many  synonymous 
terms  as  you  please,  you  will  change  his  words 
only,  but  not  his  language,  for  he  can  know 
but  one.  No  sooner  have  they  gone  through 
the  rudiments  of  the  grammar,  of  which  they 
absolutely  understand  nothing,  than  they  are 
set  to  render  a  discourse  spoken  in  their  native 
tongue  into  Latin  words ;  when  they  are  ad- 
vanced a  little  farther,4liey  are  engaged  to  patch 
up  a  theme  in  prose^by  tacking  together  the 
phrases  of  Cicero,  and  in  verse  with  centos  from 
Virgil.  They  then  be^n  to  think  themselves 
capable  of  talking  Latin.  And  who  is  there  to 
contradict  them.* 

To  learn  a  language  grammatically,  or  even 
to  speak  it,  allowing  for  bad  pronunciation,  is 

*  Rousseau,  b.  2. 


TIIE  YOUNG  MECHANIC. 


at  any  time  of  life  an  easy  acquisition.   We  are 
told  that  Themistocles  learnt  the  Persian  lan- 
guage in  one  year,  and  a  year  is  sufficient  time 
to  learn  any  language.     It  is  too  great  an  atten- 
tion to  the  rules  of  grammar  which  retards  our 
improvement.   Rousseau  has  therefore  properly 
warned  us  against  correcting  the  grammatical 
errors  of  children,  who  never  fail  in  due  time 
to  correct  themselves.     Mr.  Locke  recommends 
the  same  method  to  be  adopted  in  learning  the 
dead  languages.     "  The  Latin  tongue,"  he  ob- 
serves, "  would  easily  be  taught,  if  the  tutor 
being  constantly   with  his    pupil  would  talk 
nothing  else  to  him,  and  make  him  answer  still 
in  the  same  language."     But  to  this  reasoning  I 
object  ;  for,  not  to  mention  the  difficulty  of  find- 
ing tutors  who  can  speak  these  languages  well, 
it  is  the  constant  daily  habit  of  conversing  with 
every  one  around  us,  which  facilitates  the  ac- 
quisition of  living  tonrues,  and  this  is  particu- 
larly the  case  with  chmlren,  who  learn  more  in 
one  hour's  game  of  play  with  their  equals,  than 
in  a  day's  discourse  with  their  tutors.   Another 
strong  objection  to  this  method  arises  from  its 
inutility.     The  only  use  of  learning  the  dead 
languages  is,  as  Milton  says,  to  "  study  the 
sojid  things  in  them."     Now  even  allowing 


ON  LEARNING  A  LANGUAGE.  £73 

that  a  pupil  may  be  competent  to  hold  a  con- 
versation in  Latin,  which  certainly  is  making  a 
great  allowance,  if  we  take  into  consideration 
the  difficulty  of  applying  an  ancient  language 
to  modern  customs,  yet  he  will  reap  but  little 
benefit  from  this  acquisition  when  he  comes 
to  read  the  philosophic  works  of  Cicero,  or 
Quintilian,  or  the  histories  of  Livy  or  Tacitus. 
The  same  reasoning  is  in  some  measure  appli- 
cable to  modern  tongues.  A  foreigner  who  can 
speak  English  well,  may  be  unable  to  compre- 
hend either  the  sublime  beauties  of  Shakspeare, 
or  the  nervous  eloquence  of  Johnson.  But 
though  I  dissent  from  Mr.  Locke  as  to  the  best 
means  of  acquiring  the  dead  languages,  yet  of 
the  method  which  I  am  now  about  to  propose, 
I  speak  with  the  greater  confidence,  being  sup- 
ported in  my  opinion  not  only  by  my  own  ex- 
perience, but  by  the  practice  of  Roger  Ascham, 
the  celebrated  tutor  to  Queen  Elizabeth.  The 
custom  established  in  scnools  of  obliging  the 
scholars  to  learn  the  grammar  by  heart,  cannc  t 
be  too  much  deprecated.  The  grammar,  like 
the  dictionary,  is  only  a  book  of  reference  ;  uu> 
read  it  therefore  by  itself,  is,"  as  Ascham  well 
observes,  "  tedious  for  the  master,  hard  for  the 
scholar,  cold  and  uncomfortable  for  them  both.'7 


274  THE  "VOTING  MECHANIC. 

It  certainly  is  irksome  for  boys  who  have  it  to 
learn,  because  it  conveys  no  pleasurable  ideas, 
and  much  time  is  thus  unnecessarily  lost.  Mr. 
Dyer  in  his  life  of  Robinson,  has  observed  that 
"  Mr.  Robinson's  way  of  acquiring  a  knowledge 
of  languages,  was  to  sit  down  to  an  author, 
without  any  previous  knowledge  of  the  gram- 
mar, and  to  refer  only  to  it  in  the  same  manner 
as  the  dictionary."  This  being  premised,  let 
us  now  suppose  that  my  pupil  is  to  be  instruct- 
ed in  the  Greek  language.  He  accordingly 
procures  a  grammar  and  dictionary ;  but  instead 
of  labouring  a  twelvemonth  in  committing  the 
former  to  memory,  he  reads  it  over  once  or 
twice  merely  to  acquire  some  little  insight  into 
the  nature  of  the  language.  His  tutor  then 
procures  for  him  the  best  work  of  the  purest 
Greek  writer ;  suppose  the  Republic  of  Plato, 
or  the  Cyropaedia  of  Xenophon,  which  is  bet- 
ter adapted  to  youth.  We  now  sit  down  to- 
gether, with  our  pens,  ink  and  paper,  to  translate 
one  of  the  easiest  passages,  making  due  refer- 
ence to  our  grammar  and  dictionary.  Having 
done  this  we  shut  our  books,  and  put  our 
translations  carefully  by  in  our  drawers.  We 
then  proceed  to  other  business ;  perhaps  to  the 
carpenter's  chest,  or  the  garden  tools.  The 


ON  LEARNING  A  LANGUAGE.  275 

next  morning  we  take  out  our  translations,  and 
retranslate  them  into  the  best  Greek  we  are 
able,  which  we  compare  with,  and  correct  by 
the  original  text.  This  translation  and  retrans- 
lation,  increasing  gradually  in  quantity,  we  con- 
tinue to  practise,  till  we  become  masters  of  the 
language,  never  omitting  a  single  day,  how 
small  soever  be  the  portion.  It  should  be  re 
membered,  that,  as  we  increase  in  knowledge* 
the  version  of  one  day  is  not  retranslated  till 
the  interval  of  three  or  four  days  has  elapsed, 
in  order  that  the  pupil  may  not  translate  by 
rote.  By  these  means  the  language  is  learnt 
not  only  with  greater  facility,  but  to  much 
greater  perfection ;  for  the  scholar  acquires  a 
knowledge  of  the  peculiar  cast  of  the  language, 
and  the  particular  points  in  which  it  differs 
from  his  own.  Another  advantage  attending 
this  system  of  translation,  is,  that  the  pupil 
cannot  suffer  from  the  ignorance  of  his  tutor, 
both  of  them  having  the  best  possible  standard 
for  their  guide.  Nor  perhaps  is  it  a  matter  of 
small  importance  that  the  tutor  is  improving 
himself,  at  the  very  time  that  he  is  instructing 
his  pupil ;  and  I  am  certain  that  the  appearance 
only  of  studying  one's-self,  tends  much  to  in- 
crease the  love  of  study  in  youth. 
24 


276  THE  *OUNG  MECHANIC. 

In  addition  to  translating,  we  must  not  omit 
to  mention  the  advantages  which  accrue.,  par- 
ticularly to  maturer  minds,  from  reading  and 
reciting  the  works  of  the  great  masters.  By 
this  we  imbibe  not  only  a  taste  for  their  purity 
and  elegance  of  diction,  but  frequently  partici- 
pate of  their  animation,  and  the  fire  of  their 
genius.* 

Let  none  despair  of  acquiring,  not  only  a 
competent  but  a  critical  knowledge  of  language, 
at  whatever  age  a  taste  for  such  studies  may  be 
imbibed.  Julius  Scaliger,  a  profound  critic, 
knew  not  the  letters  of  the  Greek  alphabet  at 
the  age  of  forty  years.  Dr.  Franklin  learnt  to 
speak  French  when  upwraros  of  seventy.  Eu- 
gene Aram,  without  any  assistance,  learnt  Latin, 
Greek,  Hebrew,  French,  Chaldee,  Arabic,  and 
the  Celtic. 

Whatever  be  the  advantages,  or  defects  of 
the  English  language,  as  it  is  our  own  language, 
it  deserves  a  high  degree  of  our  study  and  at- 
tention, both  with  regard  to  the  choice  of  words 
which  we  employ,  and  with  regard  to  the  syntax, 
or  the  arrangement  of  these  words  in  a  sentence, 
V\e  know  how  much  the  Greeks  and  the  Ro* 

*  Northmore. 


THE  ENGLISH  LANGUAGE.  27*> 

mans,  in  their  most  polished  and  flourishing 
times,  cultivated  their  own  tongues.  We  know 
iiow  much  study  both  the  French  and  the  Ita- 
lians have  bestowed  on  theirs.  Whatever  know- 
ledge may  be  acquired  by  the  study  of  other 
languages,  it  can  never  be  communicated  with 
advantage,  unless  by  such  as  can  write  and 
speak  their  own  language  well.  Let  the  matter 
of  an  author  be  ever  so  good  and  useful,  his 
compositions  will  always  suffer  in  the  public 
esteem,  if  his  expression  be  deficient  in  purity 
and  propriety.  At  the  same  time,  the  attain- 
ment of  a  correct  and  elegant  style,  is  an  ob- 
ject which  demands  application  and  labour.  If 
any  imagine  they  can  catch  it  merely  by  the 
ear,  or  acquire  it  by  a  slight  perusal  of  some 
of  our  good  authors,  they  will  find  themselves 
much  disappointed.  The  many  errors,  even  in 
point  of  grammar,  the  many  offences  against 
purity  of  language,  which  are  committed  by 
writers  who  are  far  from  being  contemptible, 
demonstrate,  that  a  careful  study  of  the  lan- 
guage is  previously  requisite,  in  all  who  aim 
at  writing  it  properly.* 

The  application  of  a  child  to  a  dead  Ian- 

*Dr  Blair. 


278  THE  YOUNG  MECHANIC. 

guage,  before  he  be  acquainted  with  his  own, 
is  a  lamentable  waste  of  time,  and  highly  de- 
trimental to  the  improvement  of  his  mind.  The 
general  principles  of  grammar  are  common  to 
all  languages  •,  a  noun  is  the  same  in  English, 
French,  Latin,  Greek,  &,c.  The  varieties  of 
languages  are  easily  acquired  by  observation 
and  practice,  when  a  preliminary  knowledge  of 
our  own  grammar  is  obtained.  But,  the  com- 
prehension of  our  native  tongue,  is  not  the 
only  good  preparative  for  the  study  of  other 
languages.  Some  previous  acqaintance  with 
the  general  nature  of  things  is  necessary  to  the 
accomplishment  of  this  end,  in  order  that  our 
literary  progress  may  not  be  obstructed  merely 
by  words.  For,  although  it  be  useful  to  leave 
some  difficulties  in  the  way  of  a  child,  that  he 
may  exercise  his  mind  in  overcoming  them,  yet 
he  must  not  be  disgusted  by  too  many  or  too 
great  impediments.  Our  whole  attention  should 
consist  in  proportioning  the  difficulties  to  his 
powers,  and  in  offering  them  to  his  considera- 
tion individually.  If  Latin  were  made  the  pri 
mary  object  of  a  child's  lesson,  he  would  lose 
a  vast  portion  of  time  in  the  study  of  grammar ; 
he  would  be  incapable  of  perceiving  the  beau- 
ties of  that  language,  because  he  would  not 


THE  EJVGLISH  LANGUAGE.  £7Q 

have  acquired  any  previous  knowledge.  No 
benefit  therefore  could  possibly  accrue,  from 
reading  in  the  Latin  tongue  subjects  which  he 
could  not  understand  in  his  own.  But,  by  his 
becoming  well  acquainted  with  our  best  poets 
and  prose  writers,  he  will  easily  learn,  inde- 
pendently of  the  number  of  ideas  which  he 
will  gain  thereby,  the  general  rules  of  gram- 
mar ;  several  examples  will  unfold  them,  and  a 
proper  application  of  others  may  be  soon  made 
without  difficulty.  Besides,  he  will  acquire 
taste  and  judgment,  and  be  well  prepared  to 
•  feel  the  beauties  of  a  foreign  tongue,  when  he 
begins  to  feel  the  beauties  of  his  own.  His 
knowledge  being  also  extended  and  diversified, 
it  will  be  found  that  the  sole  difficulty  attendant 
on  the  study  of  Latin,  consists  in  learning 
words ;  so  that  to  obtain  a  just  knowledge  of 
things  he  must  apply  himself  to  such  Latin 
authors  only  as  are  within  the  reach  of  his 
capacity,  and  whose  writings  he  can  compre- 
hend with  the  same  facility  as  if  they  were 
written  in  his  native  language.  By  this  plan, 
he  will  easily  acquire  the  Latin  tc  ngue,  trea- 
sure up  fresh  knowledge  as  he  advances,  and 
experience  no  disgusts  in  the  study  of  it. 
Nothing  can  be  more  useless  than  to  fatigue  a 
24* 


280  THE  YOUNG  MECHANIC 

child,  by  filling  his  memory  with  the  rules  of 
a  language  which  he  does  not  yet  understand, 
for,  of  what  advantage  is  the  knowledge  of  its 
rules,  if  he  be  unable  to  apply  them  ?  We 
should  wait,  therefore,  until  reading  has  gradu- 
ally enlightened  his  mind,  and  the  task  becomes 
not  irksome  to  him.  When  he  has  studied  his 
own  language,  we  should  anticipate  the  princi- 
pal difference  between  the  Latin  and  English 
syntax.  His  surprise  in  perceiving  an  unex- 
pected difference,  will  excite  his  curiosity,  and 
effectually  remove  all  distaste.  After  this,  and 
not  before,  we  may  devote  a  part  of  each  day 
to  Latin ;  but  it  ought  never  to  be  the  first  ob- 
ject of  his  studies.*  The  best  English  Gram 
mar  for  the  purpose  of  self  instruction  is  Frost's 
Practical  Grammar,  published  by  Thomas, 
Cowperthwait  &.  Co.,  Philadelphia. 

The  Latin  authors  are  possessed  of  uncom- 
mon excellence.  One  kind  of  excellence  they 
possess  which  is  not  found  in  an  equal  degree 
in  the  writers  of  any  other  country  :  an  exqui- 
site skill  in  the  use  of  language ;  a  happy  se- 
lection of  words ;  a  beautiful  structure  of 
phrase  •,  a  transparency  of  style ;  a  precision 

*  H.  R.  Yorke. 


THE  LATIN  LANGUAGE.  gg] 

by  which  they  communicate  the  strongest  sen- 
timents in  the  directest  form ;  in  a  word,  even7 
thing  which  relates  to  the  most  admirable 
polish  of  manner.  Other  writers  have  taken 
more  licentious  flights,  and  produced  greater 
astonishment  in  their  readers.  Other  writers 
have  ventured  more  fearlessly  into  unexplored 
regions,  and  cropped  those  beauties  which  hang 
over  the  brink  of  the  precipice  of  deformity. 
But  it  is  the  appropriate  praise  of  the  best  Ro- 
man authors,  that  they  scarcely  present  us  with 
one  idle  and  excrescent  clause,  that  they  con 
tinually  convey  their  meaning  in  the  choicest 
words.  Their  lines  dwell  upon  our  memory; 
their  sentences  have  the  force  of  maxims,  every 
part  vigorous,  and  seldom  any  thing  which  can 
be  changed  but  for  the  worse.  We  wander  in 
a  scene  where  every  thing  is  luxuriant,  yet 
every  thing  vivid,  graceful  and  correct. 

It  is  commonly  said,  that  you  may  read  the 
works  of  foreign  authors  in  translations.  But 
the  excellencies  above  enumerated  are  incapa- 
ble of  being  transfused.  A  diffuse  and  volumi- 
nous author,  whose  merit  consists  chiefly  in 
his  thoughts,  and  little  in  the  manner  of  attiring 
them,  may  be  translated.  But  who  can  trans- 
late Horace  ?  who  endure  to  read  the  transla- 


2S2  THE  YOUNG  MECHANIC. 

tion  ?  Yet  who  is  there,  acquainted  with  hinv 
only  through  this  medium,  but  listens  with 
astonishment  and  incredulity  to  the  encomiums 
he  has  received  from  the  hour  his  poems  were 
produced  ?  The  Roman  historians  are  the  best 
which  ever  existed.  The  dramatic  merit  and 
the  eloquence  of  Livy ;  the  profound  philoso- 
phy of  Sallust;  the  rich  and  solemn  pencil  of 
Tacitus,  all  ages  of  the  world  will  admire. 
Add  to  this,  that  the  best  ages  of  Rome  afford 
the  purest  models  of  virtue  which  are  any 
where  to  be  met  with.  Mankind  are  too  much 
inclined  to  lose  sight  of  all  which  is  heroic, 
magnanimous  and  public  spirited.  Modern 
ages  have  formed  to  themselves  virtue,  rather 
polished  than  sublime,  which  consists  in  petty 
courtesies,  rather  than  in  the  tranquil  grandeur 
of  an  elevated  mind.  It  is  by  turning  to  Fabri- 
cius,  and  men  like  Fab riciusy  that  we  are  brought 
to  recollect  what  human  nature  is.  Left  to 
ourselves,  we  are  apt  to  sink  into  effeminacy 
and  apathy.  It  is  by  comparison  only  that  we 
can  enter  into  the  philosophy  of  language.  It 
is  by  comparison  only  that  we  can  separate 
ideas,  and  the  words  by  which  those  ideas  are 
ordinarily  conveyed.  It  is  by  collating  one 
language  with  another  that  we  detect  all  the 


THE  LATIN  LANGUAGE.  2S3 

shades  of  meaning  through  the  various  inflec- 
tions of  sense  which  the  same  word  suffers,  as 
it  shall  happen  to  be  connected  with  different 
topics. 

He  who  is  acquainted  with  only  one  lan- 
guage, will  probably  always  remain  in  some 
degree  the  slave  of  language.  From  the  im- 
perfectness  of  his  knowledge,  he  will  feel  him- 
self at  one  time  seduced  to  say  what  he  did 
not  mean,  and  at  another  time  will  fall  into 
errors  of  this  sort  without  being  aware  of  it. 
It  is  impossible  he  should  understand  the  full 
force  of  words.  He  will  sometimes  produce 
ridicule  where  he  intended  to  produce  passion. 
He  will  search  in  vain  for  the  hidden  treasures 
of  his  native  tongue.  He  will  never  be  able  to. 
2m ploy  it  in  the  most  advantageous  manner. 
He  cannot  be  well  acquainted  with  its  strength 
and  weakness.  He  is  uninformed  respecting 
its  true  genius  and  discriminating  characteris- 
tics. But  the  man  who  is  competent  to,  and 
exercised  in  the  comparison  of  languages,  has 
attained  to  his  proper  elevation.  Language  is 
not  his  master,  but  he  is  the  master  of  language. 
Things  hold  their  just  order  in  his  mind  ;  ideas, 
first,  and  then  words.  Words  therefore  are 
used  by  him  as  the  means  of  communicating 


284  THE  YOUNG  MECHANIC. 

or  giving  permanence  to  his  sentiments ;  and 
t.he  whole  magazine  of  his  native  tongue  is  sub- 
jected at  his  feet. 

Latin  is  a  language  which  will  furnish  us 
with  the  etymology  of  many  of  our  own 
words ;  but  it  has  perhaps  peculiar  recommen- 
dations as  a  praxis  in  the  habits  of  investiga- 
tion and  analysis.  Its  words  undergo  an  un- 
common number  of  variations  and  inflexions. 
These  inflections  are  more  philosophically  ap- 
propriated, and  more  distinct  in  their  meaning, 
than  the  inflections  of  any  language  of  a  more 
ancient  date.  As  the  words  in  Latin  composi- 
tion are  not  arranged  in  a  philosophical  or  na- 
tural order,  the  mind  is  obliged  to  exert  itself 
to  disentangle  the  chaos,  and  is  compelled  to 
yield  an  unintermitted  attention  to  the  inflec- 
tions. It  is  therefore  probable  that  the  philoso- 
phy of  language  is  best  acquired  by  studying 
this  language.  Practice  is  superior  to  theory ; 
and  this  science  will  perhaps  be  more  success- 
fully learned,  and  more  deeply  imprinted,  by 
the  perusal  of  Virgil  and  Horace,  than  by  read 
ing  a  thousand  treatises  on  universal  grammar. 
Examples  seem  to  correspond  to  what  is  here 
stated.  Few  men  have  written  English  with 
force  and  propriety,  who  have  been  wholly 


THE  LATIN  LANGUAGE.  285 

unacquainted  with  the  learned  languages  Our 
finest  writers  and  speakers  have  been  men  who 
amused  themselves  during  the  whole  of  their 
lives  with  the  perusal  of  the  classics.  Nothing 
is  generally  more  easy  than  to  discover  by  his 
style  whether  a  man  has  been  deprived  of  the 
advantages  of  a  literary  education.  He  who 
has  not  been  accustomed  to  refine  on  words, 
and  discriminate  their  shades  of  meaning,  will 
think  and  reason  after  a  very  inaccurate  and 
slovenly  manner. 

Two  qualities  are  especially  necessary  to 
any  considerable  improvement  of  human  un- 
derstanding ;  an  ardent  temper,  and  a  habit  of 
thinking  with  precision  and  order.  The  study 
of  the  Latin  language  is  particularly  conducive 
to  the  production  of  the  last  of  these  qualities. 
In  this  respect  the  study  of  Latin  and  geometry 
might  perhaps  be  recommended  for  a  similar 
reason.  In  the  study  of  language  and  its  in- 
flections, all  is  in  order.  Every  thing  is  sub- 
jected to  the  most  inflexible  laws.  The  mind 
therefore  which  is  accustomed  to  it,  acquires 
habits  of  order,  and  of  regarding  things  in  a 
state  of  clearness,  discrimination,  and  arrange- 
ment. 

The  discipline  of  mind,  here  described,  is 


286  THE  YOUNG  MECHANIC 

of  inestimable  value.  He  who  is  not  initiated 
in  the  practice  of  close  investigation  is  con- 
stantly exposed  to  the  danger  of  being  deceived. 
His  opinions  have  no  standard,  but  are  entirely 
at  the  mercy  of  his  age,  his  country,  the  books 
he  chances  to  read,  or  the  company  he  happens 
to  frequent.  His  mind  is  a  wilderness.  It  may 
contain  excellent  materials,  but  they  are  of  no 
use.  He  is  unable  to  regulate  his  mind,  and 
sails  at  the  mercy  of  every  breath  of  accident 
or  caprice.  Such  a  person  is  ordinarily  found 
incapable  of  application  or  perseverance.  All 
talent  may  perhaps  be  affirmed  to  consist  of 
analysis  and  dissection,  the  turning  a  thing  on 
all  sides,  and  examining  it  in  all  its  variety  ol 
views.  An  ordinary  man  sees  an  object  just  as 
it  happens  to  be  presented  to  him,  and  sees  no 
more.  But  a  man  of  genius  takes  it  to  pieces, 
inquires  into  its  cause  and  effects,  remarks  its 
internal  structure,  and  considers  what  would 
have  been  the  result,  if  its  members  had  been 
combined  in  a  different  way,  or  subjected  to 
different  influences.  The  man  of  genius  gains 
a  whole  magazine  of  thoughts,  where  the  ordi 
nary  man  has  received  one  idea;  and  hi* 
powers  are  multiplied  in  proportion  to  the 
number  of  ideas  on  which  they  are  to  be  em- 


THE  LATIN  LANGUAGE.  g§7 

ployed.  Now  there  is  perhaps  nothing  which 
contributes  more  eminently  to  this  subtilizing 
and  multiplication  of  mind,  than  an  attention 
to  the  structure  of  language. 

Let  it  be  taken  for  granted  that  the  above  ar- 
guments sufficiently  establish  the  utility  of 
classical  learning ;  it  remains  to  be  determined 
whether  it  be  necessary  that  it  should  form  a 
part  of  the  education  of  youth.  It  may  be 
alleged,  that,  if  it  be  a  desirable  acquisition,  it 
may  with  more  propriety  be  made  when  a  per- 
son is  arrived  at  years  of  discretion;  that  it  will 
then  be  made  with  less  expense  of  labour  and 
time,  that  the  period  of  youth  ought  not  to  be 
burdened  with  so  vexatious  a  task,  and  that  our 
early  years  may  be  more  advantageously  spent 
in  acquiring  the  knowledge  of  things,  than  of 
words.  In  answer  to  these  objections  it  may 
be  remarked,  that  it  is  not  certain  that,  if 
the  acquisition  of  the  rudiments  of  classical 
learning  be  deferred  to  our  riper  years,  it  will 
ever  be  made.  It  will  require  strong  inclina- 
tion and  considerable  leisure.  A  few  active  and 
determined  spirits  will  surmount  the  difficulty ; 
but  many  who  would  derive  great  benefit  from 
the  acquisition,  will  certainly  never  arrive  at  it. 
The  age  of  youth  seems  particularly  adapted 
25 


THE  YOUNG  MECHANIC 


to  the  learning  of  words.  The  judgment  is 
then  small,  but  the  memory  is  retentive.  In  our 
riper  years  we  remember  passions,  facts,  and 
arguments  ;  but  it  is  for  the  most  part  in  youth 
that  we  retain  the  very  words  ir»  which  they 
are  conveyed.  Youth  easily  contents  itself 
with  this  employment,  especially  where  it  is 
not  enforced  with  particular  severity.  Acquisi- 
tions which  are  disgustful  in  riper  years,  art 
often  found  'to  afford  young  persons  no  con 
Cemptible  amusement.  It  is  not  perhaps  true 
that,  in  teaching  languages  to  youth,  we  are 
imposing  on  them  an  unnecessary  burden.  ]f 
we  would  produce  right  habits  in  the  mind,  it 
must  be  employed.  Our  early  years  must  not 
be  spent  in  lethargic  indolence.  An  active  ma- 
turity must  be  preceded  by  a  busy  childhood. 

It  has  often  been  said  that  classical  learning 
is  an  excellent  accomplishment  m  men  devoted 
to  letters,  but  that  it  is  ridiculous,  in  parents 
whose  children  are  destined  to  more  ordinary 
occupations,  to  desire  to  give  them  a  superficial 
acquaintance  with  Latin,  which  in  the  sequel 
will  infallibly  fall  into  neglect.  A  conclusion 
opposite  to  this  is  dictated  by  the  preceding 
reflections.  We  can  never  foresee  the  future 
destination  and  propensities  of  our  children; 


THE  LATIN  LANGUAGE. 

yet,  no  portion  of  classical  instruction,  however 
small,  need  be  wholly  lost.  Some  refinement 
of  mind,  some  clearness  of  thinking1,  will  al- 
most certainly  result  from  grammatical  studies. 
Though  the  language  itself  should  ever  after 
be  neglected,  some  portion  of  a  general  science 
has  thus  been  acquired,  which  can  scarcely  be 
forgotten.  Though  our  children  should  be 
destined  to  the  humblest  occupation,  that  does 
not  seem  to  be  a  sufficient  reason  for  our  de- 
nying them  the  acquisition  of  some  of  the  most 
fundamental  documents  of  human  understand- 
ing.* 

The  following  method  of  teaching  Latin,  re- 
commended by  R.  L.  Edgeworth,  F.  R.  S.,  ap- 
pears exceedingly  simple,  natural,  and  pleasing, 
and  furnishes  useful  hints  for  those  who  desire 
to  teach  themselves.  u  When  children  have  by 
gentle  degrees,  and  by  short  and  clear  conver- 
sations, been  initiated  in  general  grammar,  and 
familiarized  to  its  technical  terms,  the  first  page 
of  tremulous  Lilly  will  lose  much  of  its  horror. 
It  is  taken  for  granted,  that  the  pupil  can  read 
and  understand  English,  and  that  he  has  been 
eccustomed  to  employ  a  dictionary.  He  may 

*  Godwin's  Enquirer. 


290  TIIE  YOUNG  MECHANIC. 

now  proceed  to  translate  from  some  easy  book, 
a  few  short  sentences  :  the  first  word  will  pro- 
bably be  an  adverb  or  conjunction ;  either  of 
them  may  be  readily  found  in  the  Latin  dic- 
tionary, and  the  young  scholar  will  exult  in 
having  translated  one  word  of  Latin ;  but  the 
next  word,  a  substantive  or  verb,  perhaps  will 
elude  his  search.  Now  the  grammar  may  be 
produced,  and  something  of  the  various  termi- 
nations of  a  noun  may  be  explained.  If  musam 
be  searched  for  in  the  dictionary,  it  cannot  be 
found,  but  musa  catches  the  eye,  and  with  the 
assistance  of  the  grammar  it  may  be  shown, 
that  the  meaning  of  words  may  be  discovered 
by  the  united  helps  of  the  dictionary  and  gram- 
mar. After  some  days'  patient  continuation  of 
this  exercise,  the  use  of  the  grammar,  and  of 
its  uncouth  collection  of  words  and  syllables, 
will  be  apparent  to  the  pupil ;  he  will  perceive 
that  the  grammar  is  a  sort  of  appendix  to  the 
dictionary.  The  grammatical  formulae  may 
then,  by  gentle  degrees,  be  committed  to  me- 
mory ;  and  when  once  got  by  heart,  they  should 
be  assiduously  preserved  in  the  recollection. 
After  the  preparation  which  we  have  recom 
mended,  the  singular  number  of  a  declension 
will  be  learnt  in  a  few  minutes,  by  a  child  oi 


THE  LATIN  LANGUAGE.  29 1 

ordinary  capacity,  and  after  two  or  three  days' 
repetition,  the  plural  number  may  be  added. 
The  whole  of  the  first  declension  should  be 
well  fixed  in  the  memory  before  a  second  be 
attempted.  During  this  process  a  few  words 
at  every  lesson  may  be  translated  from  Latin  to 
English,  and  such  nouns  as  are  of  the  first  de- 
clension may  be  compared  with  musa,  and  may 
be  declined  according  to  the  same  form.  Te- 
dious as  this  method  may  appear,  it  will  in  the 
end  be  found  expeditious.  Omitting  some  of 
the  theoretic  or  didactic  part  of  the  grammar, 
which  should  only  be  read,  and  which  may  be 
explained  with  care  and  patience,  the  whole 
of  the  declensions,  pronouns,  conjugations,  the 
list  of  prepositions,  conjunctions,  interjections, 
some  adverbs,  the  concords,  the  common  rules 
of  syntax,  may  be  comprised  with  sufficient 
repetitions  in  about  two  or  three  hundred  les- 
sons of  ten  minutes  each :  that  is  to  say,  ten 
minutes'  application  of  the  scholar  in  the  pre- 
sence of  the  teacher.  A  young  boy  should 
never  be  set  to  learn  a  lesson  by  heart  when 
alone.  Forty  hours  !  Is  this  tedious  ?  If  you 
are  afraid  of  losing  time,  begin  a  few  months 
earlier ;  but  begin  when  you  will,  forty  hours 
is  surely  no  great  waste  of  time ;  th^  whole,  or 
'  25* 


292  THE  YOUNG  MECHANIC. 

even  half  of  this  short  time,  is  not  spent  in  the 
labour  of  getting  jargon  by  rote;  each  day 
some  slight  advance  is  made  in  the  knowledge 
of  tneir  combinations.  What  we  insist  on  is, 
that  nothing  be  done  to  disgust  the  pupil :  steady 
perseverance,  with  uniform  gentleness,  will  in- 
duce habit,  and  nothing  should  ever  interrupt 
the  regular  return  of  the  daily  lesson.  If  ab- 
sence, business,  illness,  or  any  other  cause,  pre- 
vent the  attendance  of  the  teacher,  a  substitute 
must  be  appointed ;  the  idea  of  relaxation  on 
Sunday,  or  a  holiday,  should  never  be  permitted. 
In  most  public  seminaries  above  one  third,  in 
some  nearly  one  half,  of  the  year  is  permitted 
to  idleness  :  it  is  the  comparison  between  severe 
labour  and  dissipation  which  renders  learning 
hateful.  Johnson  is  made  to  say,  by  one  of  his 
female  biographers,  that  no  child  loves  the  per- 
son who  teaches  him  Latin ;  yet  the  writer 
would  not  take  all  the  doctor's  fame,  and  all 
the  lady's  wit  and  riches,  in  exchange  for  the 
hourly,  unfeigned,  unremitting  friendship  which 
he  enjoys  with  a  son  who  had  no  other  master 
than  his  father.  So  far  from  being  laborious  or 
troublesome,  he  has  found  it  an  agreeable  em- 
ployment to  instruct  his  children  in  grammar 
and  the  learned  languages.  In  the  midst  *>f  a 


THE  LATIN  LANGUAGE.  293 

variety  of  other  occupations,  half  an  hour 
every  morning  for  many  years,  during  the  time 
of  dressing,  has  been  allotted  to  the  instruction 
of  boys  of  different  ages  in  languages,  and  no 
other  time  has  been  spent  in  this  employment," 
It  has  been  objected,  that  a  classical  educa- 
tion loses  time  in  acquiring  words  only,  when 
ideas  ought  to  be  acquired.  This  objection 
(though  in  a  great  measure  unjust )  would  cer- 
tainly be  without  any  colour  of  reason,  if  a 
plan  could  be  proposed  for  uniting  both  these 
purposes ;  if  by  a  proper  choice  of  books  we 
could  contrive  to  store  the  mind  at  different 
periods  with  such  useful,  moral  ideas  as  are 
adapted  to  its  capacity.  The  first  branch  of  sci- 
ence which  youth  is  capable  of  comprehending 
appears  to  be  history.  On  the  knowledge  of 
facts,  all  moral  reasoning  must  depend ;  and 
facts  learned  in  youth  are  certainly  better  re- 
tained than  those  which  are  acquired  at  any 
succeeding  period.  Young  boys  are  not  inte- 
rested in  narrative  (indeed  there  is  hardly  any 
other  kind  of  composition  which  can  engage 
them  ;)  and  I  have  generally  found  them  more 
delighted  with  true  history  and  biography,  if 
not  prolix,  than  with  poetry  or  novels.  The 
tales  of  love,  and  the  minutiae  of  private  life; 


*X)4  rHE  YOUNG  MECHANIC. 

do  not  arrest  their  attention  so  much  as  the  ad- 
ventures of  heroes,  and  the  vicissitudes  of  war. 
Now  although  learning  be  a  business  rather 
than  an  amusement,  certainly  the  more  accept- 
able it  can  be  made  to  the  pupils,  the  better. 
On  these  principles,  therefore,  1  would  venture 
to  deviate  a  little  from  the  common  order  of 
school  books,  which  schoolmasters  are  more 
anxious  to  select  for  the  purity  of  the  Latin, 
than  for  any  real  instruction  or  entertainment 
they  contain.  I  would  not  be  understood  to 
insinuate,  that  the  acquisition  of  the  language, 
in  the  most  perfect  manner,  is  not  a  primary 
object-,  but  I  am  of  opinion  "that  at  a  time 
when  books  are  read  only  to  exemplify  gram- 
matical rules,  purity  and  elegance  are  not  so 
much  required,  as  when  the  scholar  is  more 
advanced."  The  initiatory  books,  I  apprehend, 
have  little  influence  in  forming  the  taste ;  before 
that  effect  can  take  place  it  is  necessary  to  be 
master  of  the  rudiments,  to  read  the  language 
with  ease,  and  to  be  able  to  consider  it  with 
something  of  a  critical  eye.  It  may  please  the 
vanity  of  a  parent  to  be  told,  that  his  boy  is 
reading  Virgil  or  Ovid ;  and  it  may  answer  the 
master's  own.  purpose,  in  a  pecuniary  view,  to 
encourage  this  absurd  vanity ;  b'at  in  the  mean 


THE  LATIN  LANGUAGE.  ggg 

time  the  real  interest  of  the  pupil  is  sacrificed, 
For  what  can  be  more  ridiculous,  than  to  in- 
volve a  child,  who  is  yet  unacquainted  with  the 
literal  meaning-  of  words,  in  all  the  obscurities 
of  figurative  and  poetic  diction  ;  and,  before  he 
has  acquired  any  ideas  on  common  things,  to 
expect  that  he  should  feel  and  admire  the  high- 
est efforts  of  the  human  imagination  ? 

The  books  which  I  would  recommend  as 
proper  to  initiate  children  in  the  learned  lan- 
guages, should  be  plain  prose,  simple,  easy  to 
be  construed,,  and  dispensing  such  knowledge 
as  is  adapted  to  their  capacities.  I  would  lead 
them  by  just  gradations  from  unadorned  lan- 
guage, and  plain  fact,  to  elegance  of  style,  ele- 
vation of  thought,  and  more  abstract  sentiment. 
After  some  very  easy  Latin,  just  sufficient  to 
show  them  the  nature  of  construing,  I  think 
Eutropius  the  most  proper  book.  It  is  an 
abridgement  of  perhaps  the  most  important 
series  of  events  which  the  annals  of  the  globe 
can  produce ;  it  is  one  of  the  easiest  books  to 
read,  and  the  style  is  clear  and  perspicuous. 
After  Eutropius,  the  young  scholar  may  have 
an  excellent  taste  of  biography  in  the  lives  of 
Cornelius  Nepos,  which,  in  point  of  difficulty 
is  properly  the  next  step  above  Eutropius, 


296  THE  YCt>TG  MECHANIC. 

.Justin  may  be  read  with  the  greatest  advantage 
after  the  other  two :  he  is  not  remarkable  for 
the  beauty  or  elegance  of  his  style ;  but  he 
collects  so  many  useful  facts  in  the  history  of 
mankind,  and  is,  as  §  can  testify  from  expe- 
rience, so  delightful  a  book  to  boys,  that  the 
advantages  to  be  derived  from  the  perusal  of  him 
infinitely  counterbalances  this  objection.  If  the 
pupils  cannot  go  through  the  whole  of  these 
authors,  the  parts  which  they  read  may  be 
chosen  so  as  to  connect  together,  and  afford 
them  a  general  view  of  the  progress  and  termi- 
nation of  the  principal  states  of  antiquity.  Let 
them  next  read  the  most  interesting  parts  ot 
Caesar  and  Sallust,  and  some  of  Cicero's  ora- 
tions. A  good  set  of  the  ancient  maps  ought 
to  be  made  use  of  while  they  are  reading  his- 
tory ;  and  thus  Geography  will  be  insensibly 
acquired,  and  more  firmly  implanted,  than  by 
any  otner  process. 

Until  they  can  construe  such  Latin  as  Cesar's 
Commentaries  tolerably  fluently,  without  the  aid 
of  a  dictionary,  and  have  gone  at  least  on°e 
through  a  set  of  the  common  school  exercises, 
such  as  Bailey's,  no  other  language,  not  even 
Greek,  should  interfere  with  the  Latin ;  other- 
wise the  memory  will  be  confused  by  the  dif- 


THE  LATIN  LANGUAGE.  097 

ferent  grammars.  But  by  the  time  they  have 
finished  the  course  of  reading  already  specified, 
it  is  presumed  they  will  be  capable  of  under- 
standing the  study  of  Greek.  Their'minds  also 
will  now  be  matured,  and  sufficiently  cultivated 
to  relish  the  charms  of  poetry,  of  which  the 
uEneid  is  the  chastest  and  most  captivating  spe- 
cimen. To  the  discretion  of  the  master  it  may 
be  left,  how  much  of  the  <£neid  can  be  read  at 
school  with  advantage.  Some  of  the  moral 
Odes,  all  the  unexceptionable  Satires,  and  Epis- 
tles of  Horace  may  follow,  and  a  few  of  the 
Satires  of  Juvenal ;  varying  occasionally  the 
course  of  their  studies  by  an  oration  of  Tully, 
the  Cato  Major,  the  Lffilius,  or  the  Offices, 
Ovid  and  Terence  I  will  venture  to  proscribe  • 
the  former,  because  he  inculcates  licentious 
ness ;  the  latter,  knavery.  1  know  no  spirit 
sooner  caught  by  boys,  than  that  little  tricking 
disposition,  that  spirit  of  low  cunning,  which 
may  be  learned  from  some  parts  of  this  author. 
In  the  Comedies  of  Terence,  the  father  is  often 
n  fantastic  or  an  avaricious  fool ;  the  son  a  pro- 
fligate ;  and  the  servant,  who  is  the  cream  of 
the  jest,  a  complete  villain.  The  purity  of  his 
Latin,  and  the  delicacy  of  his  style,  will  not,  in 
my  estimation,  compensate  for  the  danger  which 


298  THE  YOUNG  MECHANIC. 

is  incurred  by  the  imitative  faculties  of  youth. 
As  for  Ovid,  there  is  another  objection  against 
him,  for  he  corrupts  the  taste  as  well  as  the 
morals  ;  some  part  of  the  Metamorphoses  may, 
however,  be  read  with  advantage.* 

Boys  ought  to  read  prose  well  before  they 
meddle  with  the  poets.  The  former  has  visibly 
so  much  the  advantage  of  the  latter,  with  re- 
spect to  perspicuity  and  plainness  of  style,  that 
1  cannot  but  wonder  how  the  latter  came  to 
take  place  of  the  former,  in  the  common  method 
of  the  schools.  This  looks  something  like 
teaching  young  children  to  stand  upon  their 
hands,  before  they  know  how  to  make  use  of 
their  legs.  •  Prose  is  necessary  to  teach  them  a 
proper  Latin  style ;  for  the  reading  of  the  poets 
can  do  them  no  kindness  in  this  respect,  but 
rather  much  hurt,  if  they  be  not  first  well  ac- 
quainted with  prose.  The  style  of  poetry  is  so 
remote  from  the  ordinary  manner  of  expres- 
sion, that  to  imitate  it  in  prose,  would  be  the 
most  ridiculous  thing  in  the  world;  and  he 
would  be  sure  to  excite  laughter,  who  should 
pretend  to  write  a  history  in  the  strain  of  Vir- 
gil's ^Eneid,  or  Horace's  Lyrics.  To  prevent 

*  Gregory's  Essays- 


THE  LATIN  LANGUAGE.  299 

iherefore  their  confounding  those  two  different 
styles,  it  will  be  necessary  to  make  them  read 
the  historians  well  in  the  first  place  :  by  so 
doing,  they  will  learn  the  genuine  and  proper 
signification  of  words,  and  use  them  acccrd- 
ingly  :  they  will  not  be  misled  by  the  figurative 
use  of  words,  phraseology,  and  forms  of  con- 
struction proper  only  for  poetry  ;  nor  need  they 
fear  to  imitate  the  language  of  their  authors ; 
whereas,  in  the  reading  of  the  poets,  the  case 
would  be  otherwise ;  there  they  could  borrow 
nothing,  without  rendering  their  style  very 
bombastic  arid  ridiculous.* 

The  author  of  "  Stemmata  Latinitatis"  has 
conferred  an  essential  service  on  the  public  ;  but 
still  there  is  wanting  a  dictionary  for  schools, 
in  which  elegant  and  proper  English  might  be 
substituted  for  the  barbarous  translations  now 
in  use.  Such  a  dictionary  could  not  be  com- 
piled, we  think,  without  an  attention  to  the 
course  of  books  which  are  most  commonly 
used  in  schools.  The  first  meanings  given  in 
the  dictionary  should  suit  the  first  authors 
which  a  boy  reads;  this  may  probably  be  a 
remote  or  metaphoric  meaning  :  then  the  radical 


*  Clarke's  Essay  on  Education,  1730. 
26 


300  TIIE  YOUNG  MECHANIC. 

word  should  be  mentioned,  and  it  would  not 
cost  a  master  any  great  trouble  to  trace  the 
genealogy  of  words  to  the  parent  stock. 

Cordery  is  a  collection  of  such  mean  sen- 
tences, and  uninstructive  dialogue,  as  to  be 
totally  unfit  for  boys.  Commenius's  u  Visible 
World  Displayed"  is  far  superior,  and  might, 
with  proper  alterations  and  better  prints,  be- 
come a  valuable  English  school  book.  Both 
these  works  were  intended  for  countries  where 
the  Latin  language  was  commonly  spoken,  and 
consequently  they  are  filled  with  the  terms  ne- 
cessary for  domestic  life  and  conversation  :  for 
this  very  reason  they  are  not  good  introduc- 
tions to  the  classics.  Selections  from  Bailey's 
Phoedrus  will  be  proper  for  young  beginners  on 
account  of  the  glossary.  We  prefer  this  mode 
of  assisting  them  with  glossaries  to  the  use  of 
translations,  because  they  do  not  induce  indo- 
lent habits,  and  yet  they  prevent  the  pupil  from 
having  unnecessary  labour.  Translations  always 
give  the  pupil  more  trouble  in  the  end,  than 
they  save  in  the  beginning.  The  glossary  to 
Bailey's  Phoedrus,  which  we  have  just  mention- 
ed, needs  much  to  be  modernized,  and  the  lan- 
guage requires  to  be  improved.  Mr.  Valpy's 
Select  Sentences  would  be  far  more  useful  if 


THE  LATIN  LANGUAGE.  3Ql 

« 

they  had  a  glossary  annexed.  As  they  are, 
they  will  however  be  useful  after  Phcedrus. 
Ovid's  Metamorphoses,  with  all  its  monstrous 
faults,  appears  to  be  the  best  introduction  to 
the  Latin  classics,  and  to  heathen  mythology. 
Norris's  Ovid  may  be  safely  put  into  the  hands 
of  children,  as  it  is  a  selection  of  the  least  ex- 
ceptionable fables.  Cornelius  Nepos,  a  crab- 
bed book,  but  useful  from  its  brevity,  and  from 
its  being  a  proper  introduction  to  Grecian  and 
Roman  history,  may  be  read  nearly  at  the  same 
time  with  Ovid's  Metamorphoses.  After  Ovid 
the  pupil  may  begin  Virgil,  postponing  some 
of  the  Eclogues,  and  all  the  Georgics.* 

To  write  exercises  in  Latin  appears  essential- 
ly necessary  to  grammatical  perfection,  and 
should  commence  as  soon  as  the  pupil  has 
gone  through  the  syntax.  I  do  not  feel  con- 
vinced of  the  propriety  or  advantage  of  com- 
posing in  verse.  That  several  excellent  writers 
had  been  accustomed  to  write  Latin  verses  in 
their  youth,  is  far  from  amounting  to  a  proof  in 
its  favour,  because  there  is  great  probability, 
that  those  men  would  have  excelled,  whether 
they  had  written  verses  at  school  or  not.  That 

*  Mr.  R.  L.  Edgeworth. 


302  THE  YOUNG  MECHANIC. 

to  write  in  verse  facilitates  and  improves  oui 
prose,  I  think  admits  of  dispute.  I  am  sure  it 
cannot  answer  the  end  of  accustoming  the  stu- 
dent to  perspicuity  and  precision,  or  of  perfect- 
ing him  in  grammar ;  t.nd  I  apprehend  it  will 
rather  serve  to  induce  a  loose  and  vicious  mode 
of  composition,  and  lead  him  to  attend  more  to 
sound  than  sense.  It  cannot  be  denied,  that 
this  practice  takes  up  much  more  time  than  a 
common  exercise ;  and  if  it  answer  no  particu- 
lar purpose,  why  waste  that  time,  which  might 
be  more  usefully  employed  in  the  acquisition 
of  ideas  ?  The  very  mention  of  stringing 
words  together  without  order  or  meaning,  which 
is  always  the  commencement,  and  too  often 
the  conclusion,  of  school  versification,  implies 
something  ridiculous  if  not  pernicious.  But  I 
will  grant  that  a  genius  for  poetry  may  receive 
some  improvement  from  composing  in  verse 
when  young ;  whether  that  be  a  desirable  con- 
sequence or  not,  thobe  who  are  parents  must 
determine.  How  few  poets  are  so  happy  as  to 
succeed  !  and  even  when  successful,  how  bar- 
ren, how  uncertain  are  the  rewards  of  genius ! 
The  enthusiasm  of  poetry  incapacitates  us  for 
most  other  employments,  nor  is  the  unsuccess- 
ful adventurer  easily  reduced  to  his  sober 


THE  LATIN  LANGUAGE.  393 

senses  :  he  contends  in  the  face  of  poverty,  ac- 
companied with  contempt ;  and  pursues  his  itch 
of  scribbling  through  innumerable  disappoint- 
ments, without  even  the  airy  premium  of  ap- 
plause. I  have  heard  it.  urged  further,  in  de- 
fence of  these  poetic  exercises,  that  they  teach 
boys  quantity  and  pronunciation.  But  surely 
they  never  can  be  necessary  on  this  account,  if 
the  master  be  careful  from  the  first  to  accustom 
the  learner  to  a  right  pronunciation ;  and  were 
not  this  sufficient,  the  end  would  be  fully  an- 
swered by  a  practice,  which  I  think  as  salutary 
as  the  other  is  pernicious  ;  I  mean  that  of  com- 
mitting to  memory  some  of  the  moral  passages 
of  Virgil,  Horace,  and  the  best  of  the  poets. 
This  will  serve  at  once  to  furnish  the  mind  with 
words  and  with  ideas ;  and  will  implant  pre- 
cepts in  the  heart,  which  may  be  useful  through 
all  the  different  periods  of  life.  If  it  cannot  im- 
part taste,  it  will  improve  it.  It  will  infix  in 
the  mind  the  best  rules  of  grammar  in  indelible 
characters.* 

It  was  with  much  regret  that  the  compiler 
met  with  the  following  illiberal  reflect]  ans  by 
the  enlightened  and  ingenious  Doctor  Knox 


*  Gregory's  Essays 

26* 


304  THE  YOUNG  MECHANIC. 

"  Some  writers  on  the  subject  of  education 
have  expressed  themselves  against  the  general 
practice  of  composing  Latin  verse  at  schools, 
with  a  degree  of  acrimony,  which  has  led  their 
readers  to  conclude,  that  they  themselves  were 
ignorant  of  the  art,  and  without  a  taste  for  its 
beauties.  I  imagine  too,  that  some  of  them 
never  had  a  truly  classical  education  at  a  public 
school,  or  were  members  of  either"  English 
university."  Liberal  Education,  page  65,  edit. 
1783.  Again,  "  Such  objections  appear  very 
plausible  to  illiterate  persons,  and  those  very 
many  who  know  not  what  a  classical  education 
means,  or  what  advantages  it  tends  to  produce  !" 
Page  68.  In  the  same  work,  page  284,  Dr. 
Knox  acknowledges,  that  Mr.  Locke,  who  wrote 
decidedly  against  boys  making  verses  at  school, 
•was  a  student  of  Christ  Church  College,  Ox- 
ford ;  and  wrote  there  some  Latin  verses  ad- 
dressed to  Cromwell.  But  he  also  remarks, 
that  "  Locke  was  led  to  differ  from  others  on 
the  subject  of  education  from  a  warmth  of  re- 
forming spirit."  Those  assertions  do  not  ap- 
pear well  founded,  for  Locke  produced  his 
"  Thoughts  on  Education"  at  the  age  of  fifty- 
eight.  It  might  therefore  be  said  with  greater 
plausibility,  that  his  decisions  on  this  subject. 


THE  GREEK  LANGUAGE.  3Q5 

were  the  result  of  much  experience,  mature 
judgment,  and  cool  discrimination. 

The  assertion  will  not  perhaps  be  liable  to 
be  controverted  by  those,  who  are  best  ac- 
quainted with  such  subjects,  and  are  best  qua- 
lified to  make  extensive  and  just  comparisons, 
if  it  be  said  that  the  Greek  claims  the  supe- 
riority over  all  other  languages.  In  its  nume- 
rous modes  of  expression  there  is  precision 
without  obscurity,  and  copiousness  without 
redundance.  It  owes  the  former  to  the  various 
and  diversified  inflections  of  its  words,  and  the 
latter  to  its  great  number  of  derivatives.  In  its 
general  structure  and  formation,  a  proper  re- 
gard is  paid  to  the  ear,  as  well  as  to  the  under- 
standing ;  for  its  energy  and  strength  are  not 
more  striking  than  its  harmony.  The  strict- 
ness of  its  rules  does  not  impose  too  much  re-  - 
straint  upon  its  expressions,  and  its  grammati- 
cal system  is  in  every  part  exact  and  complete.* 

From  a  short  view  of  its  history  and  cha- 
racteristics, it  will  be  evident,  that  this  language 
deserves  to  be  held  up  as  a  perfect  model  of 
expression,  and  that  it  fully  justifies  the  praise 
of  those  scholars  and  critics,  who  have  cele- 

*  See  Lord  Monboddo  on  the  Origin  cf  Language,  voL 
tv.  page  25, 


306  THE  YOUNG  MECHANIC. 

brated  its  excellence  in  proportion  as  they  have 
enjoyed  its  beauties,  and  derived  taste,  improve- 
ment, and  pleasure,  from  the  perusal  of  its  in- 
comparable writers.* 

Greek  is  worth  the  pains  of  learning,  merely 
as  a  language  ;  and  I  question  whether  any  man 
can  be  an  adequate  judge  of  the  structure,  force, 
and  harmony  of  language,  who  is  totally  igno- 
rant of  it.  The  true  principles  of  taste  are  to 
be  imbibed  in  their  greatest  perfection  from  the 
Greek  writers,  whose  chastity,  perspicuity,  and 
elegance,  have  never  been  excelled,  and  very 
seldom  equalled.  In  teaching  Greek,  the  most 
proper  book  to  commence  with  is  certainly  one 
of  the  Gospels.  I  would  prefer  St.  Matthew's, 
because  I  think  it  written  in  a  more  agreeable 
and  entertaining  manner  than  that  of  St.  John, 
which  is  usually  the  first  book.  Of  the  New 
Testament,  Matthew  and  Luke  will  be  quite 
sufficient.  After  these  I  would  recommend  some 
easy  prose;  perhaps  the  Pictures  of  Cebes  would 
not  be  found  too  difficult.  A  few  of  the  Odes 
of  Anacreon,  if  selected  with  judgment,  may 
be  read.  My  predilection  for  History  inclines 
me  to  recommend  as  much  of  Herodotus  as  may 

•  Mr.  Kelt's  Elements  of  General  Knowledge. 


THE  GREEK  LANGUAGE  3Q7 

conveniently  be  read.  It  is  the  most  entertain- 
ing book  I  am  acquainted  with ;  and  much  solid 
instruction  may,  on  the  whole,  be  collected 
from  it.  The  style  is  simple  and  beautiful,  with 
this  additional  circumstance  in  its  favour,  thai 
it  is  the  best  introduction  to  Homer.  Some 
schoolmasters  may  prefer  the  Cyropaedia  of 
Xenophon,  which  is  an  excellent  book,  if  the 
boys  do  not  think  it  prolix.  It  is  almost  need- 
less to  mention,  that  the  Anabasis  is  the  best  of 
all  that  author's  works.  After  as  much  of 
Homer  as  may  be  thought  expedient,  it  may  be 
of  use  to  dip  a  little  into  the  Orations  of  Iso- 
crates,  as  introductory  to  Demosthenes,  who 
must  by  no  means  be  neglected.  Of  the  Manual 
of  Epictetus  the  master  may,  if  he  pleases, 
make  considerable  advantage,  by  taking  occa 
sion  to  explain  from  it  the  moral  philosophy  of 
the  Stoics.  Thucydides,  as  well  as  Livy  and 
Tacitus,  the  higher  poets  and  philosophers, 
must,  I  fear,  be  reserved  for  the  university ;  as 
no  school  class  can  be  expected  to  go  through 
a  greater  number  of  books  than  those  which  I 
have  already  specified.  By  pursuing  this  plan 
of  reading,  I  am  persuaded  the  student  would 
*eap  much  more  useful  knowledge,  than  by  the 
fumbled,  unsystematic  method  commonly  pur- 


308  TIIE  YOUNG  MECHANIC. 

sued  in  schools.  What,  perhaps,  he  would  be 
most  deficient  in,  would  be  the  heathen  mytho- 
logy, of  the  great  advantage  of  which  I  must 
confess  myself  ignorant.  Jn  return,  he  would 
be  master  of  all  the  leading  facts  in  the  history 
of  mankind ;  and  if  history  be  to  ethics  what 
experiment  is  to  physics,  he  would  have  laid 
the  best  foundation  of  moral  reasoning.  None 
of  the  advantages  of  classical  learning,  in  re- 
spect to  the  improvement  of  taste,  would  be 
lost  by  this  course  of  study ;  and  perhaps  the 
style  which  would  be  formed  from  the  authors 
I  have  recommended,  would  be  preferable  to 
the  prettinesses  which  is  acquired  from  reading 
poetry;  being  formed  on  the  best  models  of 
that  manly  eloquence,  which  is  the  proper  as- 
sociate and  embellishment  of  virtuous  princi- 
ples. I  have  omitted  entering  into  a  detail  of 
the  manner  in  which  I  would  have  the  rudi- 
ments taught,  because  I  do  not  in  this  respect, 
materially  differ  from  the  common  practice  of 
schools.  Before  a  boy  be  put  to  construe,  he 
should  be  well  grounded  in  the  Accidence,  per- 
fectly master  of  the  declensions  of  nouns  and 
verbs,  as  well  as  the  rules  for  determining  the 
genders,  and  the  formation  of  the  tenses.  But 
1  do  not  think  there  is  an  absolute  necessity 


THE  GRE    K  LANGUAGE.  £>Q9 

previous  to  the  reading  of  any  author,  to  over- 
charge his  memory  with  a  multitude  of  syntax 
rules,  of  the  use  and  application  of  which  he 
must  be  totally  ignorant.  The  concords,  and  a 
few  of  the  principal  rules,  will  be  quite  enough 
for  him  when  he  begins  to  construe.  He  must 
afterwards  continue  to  get  off  a  portion  of  the 
other  rules  every  day,  and  must  be  well  exer- 
cised in  the  grammar  during  the  whole  of  his 
progress. 

I  agree  with  Mr.  Knox,  that  to  teach  wholly 
by  translations  is  pernicious.  But  I  must  ob- 
serve, that  if  with  the  first  and  second  books 
which  a  child  is  put  to  construe,  no  translation 
be  made  use  of,  the  master  himself  must  be  in 
place  of  a  translation  ;  or  the  pupil  must,  at  the 
expense  of  some  of  his  pocket  money,  apply 
to  his  school-fellows.  It  is  impossible,  on  the 
first  efforts  to  construe,  to  proceed  without  some 
guide ;  or  to  use  a  dictionary  with  that  ease 
and  dexterity  which  are  essential  to  profit.  To 
allow  them  the  assistance  of  a  translation  at 
first,  and  before  they  have  acquired  a  little  stock 
of  words,  is  more  suitable  to  the  progressive 
powers  of  the  human  mind.  I  grant  there  will 
be  some  difficulty  to  be  surmounted  when  they 
first  lay  aside  the  translation ;  but  this  will  be 


310  TIIE  YOUNG  MECHANIC. 

nothing  like  so  discouraging  as  the  gloomy 
prospect  of  entering  on  a  language  totally  un- 
known, and  being  obliged  to  consult,  a  dic- 
tionary for  every  word.* 

The  modern  practice  of  teaching  Greek 
through  the  medium  of  Latin  appears  to  me 
highly  erroneous.  It  not  only  retards  the  pro- 
gress of  a  scholar,  but  it  renders  the  idioms  of 
both  languages  confused  ;  and  the  beauty  of  the 
article,  and  some  of  the  tenses,  independent  of 
other  considerations,  is  thus  entirely  lost.  The 
labours  of  literary  men  cannot  be  directed  to  a 
more  useful  purpose,  than  the  compilation  of 
*  dictionaries  and  grammars  in  the  Greek  and 
vernacular  tongues/)* 

To  the  objection  that  too  much  time  is  lost 
in  learning  the  words  of  the  sentiments  which 
we  might  obtain  by  means  of  translations,  this 
plain  answer  may  be  given,  that  a  person  can 
never  learn  a  language,  without  adding  to  the 
stock  of  his  ideas ;  and  that  the  better  the  lan- 
guage is,  (and  where  shall  we  find  any  equal  to 
the  Greek  and  Latin  ?)  the  more  correct  will  be 
the  judgment,  and  the  more  vigorous  the  per  • 
ceptions  of  the  learner.  The  learned  tonguev 

*  Gregory's  Essays.  f  Northmore. 


CLASSICAL  LEARNING.  g]_  j 

form  at  once,  even  considered  merely  in  their 
structure,  the  best  code  of  laws  for  taste,  and 
the  best  models  for  logical  reasoning  and  argu- 
ment. No  one  who  can  read  the  classics  would 
exchange  the  fruit  of  the  time  spent  upon  them 
for  any  other  attainment  which  his  earlier  years 
could  have  made.* 

The  Earl  of  Chatham  says  to  his  nephew, 
"  I  rejoice  to  hear  that  you  have  begun  Homer's 
Iliad  ;  and  have  made  great  progress  in  Virgil ; 
I  hope  you  taste  and  love  these  authors  parti- 
cularly. You  cannot  read  them  too  much, 
they  are  not  only  the  two  greatest  poets,  but 
they  contain  the  finest  lessons  for  your  age  to 
imbibe :  lessons  of  honour,  courage,  disinte- 
restedness, love  of  truth,  command  of  temper, 
gentleness  of  behaviour,  humanity,  and  in  one 
word,  virtue,  in  its  true  signification.  Go  on, 
my  dear  nephew,  and  drink  as  deep  as  you  can 
of  these  divine  springs :  the  pleasure  of  the 
draught  is  equal  at  least  to  the  prodigious  ad- 
vantages of  it  to  the  heart  and  morals.f 

There  is  yet  wanting  in  different  languages, 
says  Stevenson,  initiatory  books,  containing 

*  Edinburgh  Review,  iii.  351. 

j-  Letters  to  T.  Pitt,  Esq.,  afterwards  Lord  Camelford, 
page  6. 

27 


312  THE  YOUNG  MECHANIC. 

physical  facts,  none  of  which  would  be  dry  and 
uninteresting.  Natural  History  and  Philosophy, 
in  all  their  branches,  even  though  they  were 
superficial,  would  be  of  much  greater  use  in 
every  situation  in  life,  than  an  intimacy  with 
poetic  flights  of  imagination,  and  all  the  lumber 
of  the  heathen  mythology,  the  perusal  of  which 
affords  but  selfish,  momentary,  and  insulated 
pleasure.  Young  people  remember  facts  much 
more  readily  than  sublime  metaphor,  or  labour- 
ed sentiment.* 

Though  I  particularly  recommend  classical 
learning,  says  Dr.  Knox,  I  do  not  recommend 
it  exclusively.  I  think  it  ought  to  claim  the 
earliest  attention,  and  to  form  the  foundation ; 
because  no  other  learning  contributes  so  much 
to  open  and  to  polish  the  mind.  After  this 
polish  and  expansion  are  acquired,  and  this 
foundation  laid,  f  recommend  an  attention  to 
the  sciences,  to  natural  history  and  experimental 
philosophy,  to  botany,  to  chemistry,  to  paint- 
ing, to  architecture,  to  mechanical  works,  and 
in  general  to  all  the  productions  of  human  in- 
genuity. A  capacious  mind  will  view  the  uni- 
verse and  all  which  it  contains,  as  one  vast 

*  Remarks  on  the  inferior  utility  of  Classical  Learning 


MATHEMATICS. 

volume  laid  before  it  for  perusal.  Philology 
alone  is  comparatively  a  confined,  though  ele- 
gant attainment. 

MATHEMATICS. 

Arithmetic  may  now  be  considered  as  having 
advanced  to  a  degree  of  perfection  which  in 
former  times  could  scarcely  have  been  con- 
ceived, and  to  be  one  of  those  few  sciences 
which  have  left  little  room  for  farther  improve- 
ment. It  is,  however,  a  serious  and  almost 
general  complaint,  that  few  children,  while  at 
school,  make  any  tolerable  progress  in  arith- 
metic;  and  that  the  generality,  after  having 
spent  several  years  under  the  tuition  of  a  mas- 
ter, are  incapable  of  applying  the  few  rules 
which  they  have  learned,  to  the  useful  purposes 
of  life.  A  few  elementary  principles  are  ac- 
quired by  rote,  and  therefore  quickly  forgotten  ; 
because  the  most  essential  particulars,  namely, 
the  reasons  on  which  these  rules  are  founded, 
and  their  extensive  use  in  the  various  concerns 
of  society  are  generally  omitted,* 

So  much  of  the  science  of  numbers  as  is  in 
common  use,  as  the  numeration,  subtraction^ 

*  Dom.  Encyclopaedia. 


314  THE  YOUNG  MECHANIC. 

multiplication,  and  division  of  money,  should 
be  learnt  with  accuracy ;  to  which  should  be 
added  the  rule  of  three  and  decimal  fractions ; 
which  will  abundantly  repay  the  labour  of  ac- 
quiring them  by  the  pleasure  and  utility  which 
will  perpetually  result  from  the  knowledge  of 
them  through  life.* 

The  only  sciences  which  can  be  denominated 
pure  are  the  Mathematics.  Of  these,  every 
mechanic  and  labourer  should  be  made  ac- 
quainted with  Euclid,  particularly  the  first  six 
books ;  also  algebra ;  the  properties  of  the  conic 
sections ;  and  the  doctrine  of  fluxions.  Owing 
to  the  very  little  attention  which  is  paid  to  these 
sciences  at  present,  it  may  appear  to  many,  that 
their  study  is  attended  with  great  difficulty,  and 
little  advantage.  Neither  of  these  prejudices 
Dorders  on  the  confines  of  truth.  In  order 
that  those  sciences  may  become  capable  of  gra- 
tifying the  desire  which  children  entertain  for 
the  acquisition  of  truth  and  knowledge,  L  is 
absolutely  necessary  that  they  be  rendered  as 
clear  and  evident  as  possible,  and  also  that 
their  application  and  utility  be  made  apparent. 
Nothing  more  seems  wanting  to  render  the 
study  of  mathematics  pleasant  and  agreeable, 
*  Dr.  Darwin. 


MATHEMATICS. 

than  to  apply  them  to  those  purposes  wnich 
must  make  their  utility  and  perfection  clear 
striking,  and  interesting.  The  time  in  which 
mathematics  should  be  studied,  must  succeed 
that  of  literature.  To  comprehend  abstract  and 
general  truth,  some  energy  and  comprehension 
of  mind  are  requisite.  To  point  out  the  pre- 
cise period  when  the  study  of  mathematical 
science  should  commence,  is  attended  with  some 
difficulty.  It  must  evidently  vary,  according 
to  the  progress  which  the  mind  may  have  made 
towards  maturity  and  perfection.* 

I  agree  with  Mr.  Locke,  that  there  is  no  study 
better  fitted  to  exercise  and  strengthen  the  rea- 
soning powers,  than  that  of  the  mathematical 
sciences,  for  two  reasons ;  first,  because  there 
is  no  other  branch  of  science  which  gives  such 
scope  to  long  and  accurate  trains  of  reasoning ; 
and,  secondly,  because  in  mathematics  there  is 
no  room  for  authority,  nor  for  prejudice  of  any 
kind,  which  may  give  a  false  bias  to  the  judg- 
ment. When  a  youth  of  moderate  parts  begins 
to  study  Euclid,  every  thing  at  first  is  new  to 
him.  His  apprehension  is  unsteady ;  his  judg^ 
ment  is  feeble,  and  rests  partly  upon  the  evi- 
dence of  the  thing,  and  partly  upon  the  authority 
^  *  Dr.  Cowan. 


31 Q  THE  YOUNG  MECHANIC. 

of  his  teacher.  But  every  time  he  goes  over 
the  definitions,  the  axioms,  the  elementary  pro- 
positions, more  light  breaks  in  upon  him :  the 
language  becomes  familiar,  and  conveys  clear 
and  steady  conceptions ;  the  judgment  is  con- 
firmed ;  he  begins  to  see  what  demonstration 
is ;  and  it  is  impossible  to  see  it  without  being 
charmed  with  it.  He  perceives  it  to  be  a  kind 
of  evidence  which  has  no  need  of  authority  to 
strengthen  it.  He  finds  himself  emancipated 
from  that  bondage ;  and  exults  so  much  in  this 
new  state  of  independence,  that  he  spurns  at 
authority,  and  would  have  demonstration  for 
every  thing ;  until  experience  teaches  him,  that 
this  is  a  kind  of  evidence  which  cannot  be  had 
in  most  things ;  and  that  in  his  most  important 
concerns,  he  must  rest  contented  with  probabi- 
lity. As  he  goes  on  in  mathematics,  the  road 
of  demonstration  becomes  smooth  and  easy ; 
he  can  walk  in  it  firmly,  and  take  wider  steps : 
and  at  last  he  acquires  the  habit,  not  only  of 
understanding  a  demonstration,  but  of  discover- 
ing and  demonstrating  mathematical  truths. 
Thus,  a  man,  without  rules  of  logic,  may  ac- 
quire a  habit  of  reasoning  justly  in  mathema 
tics ;  and,  I  believe  he  may,  by  like  means,  ac- 
quire a  nabit  of  reasoning  justly  in  mechanics, 


LOGIC.  317 

in  jurisprudence,  in  politics,  or  in  any  other 


LOGIC. 

Good  sense,  good  examples  and  assiduous 
exercise,  may  bring  a  man  to  reason  justly  and 
acutely  in  his  own  profession,  without  rules. 
But  if  any  man  think,  that  from  this  concession 
he  may  infer  the  inutility  of  logic,  he  betrays  a 
great  want  of  that  art  by  this  inference  :  for  it 
is  no  better  reasoning  than  this,  that  because  a 
man  may  go  from  Edinburgh  to  London  by  the 
way  of  Paris,  therefore  any  other  road  is  use- 
less. There  is  perhaps  no  mechanic  art  which 
may  not  be  acquired,  in  a  very  considerable  de- 
gree, by  example  and  practice,  without  reducing 
it  to  rules.  But  practice,  joined  with  rules, 
may  carry  a  man  on  in  his  art  farther  and  more 
quickly,  than  practice  without  rules.  Every 
ingenious  artist  knows  the  utility  of  having  his 
art  reduced  to  rules,  and  by  that  means  made  a 
science.  He  is  thereby  enlightened  in  his  prac- 
tice, and  works  with  more  assurance.  By  rules, 
he  sometimes  corrects  his  own  errors,  and  often 
detects  the  errors  of  others :  he  finds  them  of 
great  use  to  confirm  his  judgment,  to  justify 
what  is  right,  and  to  condemn  what  is  wrong. 


318  THE  YOUNG  MECHANIC. 

Is  it  of  no  use  in  reasoning,  to  be  well  acquainted 
with  the  various  powers  of  the  human  under- 
standing, by  which  we  reason  ?  Is  it  of  no 
use.  to  resolve  the  various  kinds  of  reasoning 
into  their  simple  elements ;  and  to  discover,  as 
far  as  we  are  able,  the  rules  by  which  these 
elements  are  combined  in  judging  and  in  rea- 
soning ?  Is  it  of  no  use,  to  mark  the  various 
fallacies  in  reasoning,  by  which  even  the  most 
ingenious  men  have  been  led  into  error  ?  It 
must  surely  betray  great  want  of  understanding, 
to  think  these  things  useless  or  unimportant. 
These  are  the  things  which  logicians  have  at- 
tempted, and  which  they  have  executed ;  not 
indeed  so  completely  as  to  leave  no  room  for 
improvement,  but  in  such  a  manner  as  to  give 
very  considerable  aid  to  our  reasoning  powers. 
That  the  principles  laid  down  with  regard  to 
definition  and  division,  with  regard  to  the  con- 
version and  opposition  of  propositions  and  the 
general  rules  of  reasoning,  are  not  without  use, 
is  sufficiently  apparent  from  the  blunders  com- 
mitted by  those  who  disdain  any  acquaintance 
with  them.* 

Geometry  should  always  form  a  part  of  a 

*  Lord  Kaimes'  Sketches* 


LOGIC 

liberal  course  of  studies.  It  has  its  direct  uses 
and  its  indirect.  It  is  of  great  importance  for 
the  improvement  of  mechanics  and  the  arts  of 
life.  It  is  essential  to  the  just  mastery  of  as- 
tronomy and  various  other  eminent  sciences 
But  its  indirect  uses  are  perhaps  of  more  worth 
than  its  direct.  It  cultivates  the  powers  of  the 
mind,  and  generates  the  most  excellent  habits. 
It  eminently  conduces  to  the  making  man  a 
rational  being,  accustoms  him  to  a  closeness  of 
deduction,  which  is  not  easily  made  the  dupe 
of  ambiguity,  and  carries  on  an  eternal  war 
against  prejudice  and  imposition.*  But  geome- 
try is  not  a  competent  guide  to  the  art  of  rea- 
soning without  the  study  of  logic. 

It  is  a  very  great  error  to  suppose  that  logic 
consists  only  in  those  formal  debates  and  ver- 
bal disputations,  in  which  the  schoolmen  and 
their  fo  lowers  consumed  so  much  time  in  the 
dark  ages,  previous  to  the  revival  of  classical 
learning.  It  is  equally  a  mistake  to  imagine, 
that  it  is  merely  intended  to  teach  the  method 
of  disputing  by  rules,  and  to  instruct  a  person 
to  converse,  not  from  a  love  of  truth,  but  a 
desire  of  victory.  As  there  is  nothing  more 

*  God  win's  Enquirer. 


320  THE  YOUNG  MECHANIC. 

disingenuous  than  such  a  conduct  as  this,  no- 
thing more  unbecoming  a  rationable  being,  than 
to  oppose  sophistry  to  good  sense,  and  evasion 
to  sound  argument,  the  logician  disclaims  this 
abuse  of  the  principles  of  his  art,  and  vindi- 
cates its  rights  by  displaying  its  true  and  proper 
office.  It  is  in  reality  capable  of  affording  the 
most  important  assistance  to  the  understanding 
in  its  inquiries  after  truth ;  it  is  eminently  use- 
ful in  the  common  affairs  of  life,  and  renders 
the  greatest  service  to  science,  learning,  virtue, 
and  religion. 

Logic  is  the  art  of  forming  correct  ideas,  and 
of  deducing  right  inferences  from  them ;  or  it 
may  be  said  to  constitute  the  knowledge  of  the 
human  mind,  inasmuch  as  it  traces  the  progress 
of  all  our  information,  from  our  first  and  most 
simple  conception  of  things,  to  those  numerous 
conclusions  which  result  from  comparing  them 
together.  It  teaches  us  in  what  order  our 
thoughts  succeed  each  other,  and  it  instructs  us 
in  the  relation  which  subsists  between  our 
idras,  and  the  terms  in  which  we  express  them 
It  distinguishes  their  different  kinds,  and  points 
out  their  properties ;  discovers  the  sources  of 
our  intellectual  mistakes,  and  shows  how  we 
may  correct  and  prevent  them.  It  displays 


LOGIC.  321 

those  principles  and  rules,  which  we  follow, 
although  imperceptibly,  whenever  we  think  in 
a  manner  conformable  to  truth. 

The  faculty  of  reason  is  the  pre-eminent 
quality,  by  which  mankind  are  distinguished 
from  all  other  animals  ;  but  still  we  are  far  from 
finding  that  they  possess  it  in  the  same  degree. 
There  is  indeed  as  great  an  inequality  in  this 
respect  in  different  persons,  as  there  is  in  their 
strength  and  agility  of  body.  Nor  ought  this 
disproportion  to  be  wholly  ascribed  to  the 
original  constitution  of  the  minds  of  men,  or 
the  difference  of  their  natural  endowments  ;  for, 
if  we  take  a  survey  of  the  nations  of  the  world, 
we  shall  find  that  some  are  immersed  in  igno- 
rance and  barbarity,  others  enlightened  by 
learning  and  science ;  and,  what  is  still  more 
remarkable,  the  people  of  the  same  nation  have 
been  in  various  ages  distinguished  by  these 
very  opposite  characters.  It  is,  therefore,  by 
due  cultivation,  and  proper  diligence,  that  we 
increase  the  vigour  of  our  minds,  and  carry 
reason  to  perfection.  Where  this  method  is 
followed,  the  intellect  acquires  strength,  and 
knowledge  is  enlarged  in  every  direction ;  where 
it  is  neglected,  we  remain  ignorant  of  the  value 
of  our  own  powers;  and  those  faculties,  by 


322  THE  YOUNG  MECHANIC. 

which  we  are  qualified  to  survey  the  vast  fabric 
of  the  world,  to  contemplate  the  whole  face  of 
nature,  to  investigate  the  causes  of  things  and 
to  arrive  at  the  most  important  conclusions  as 
to  our  welfare  and  happiness,  remain  buried  in 
darkness  and  obscurity.  No  branc  i  of  science 
therefore  affords  us  a  fairer  prospect  t  f  improve- 
ment, than  that  which  relates  to  the  understand- 
ing, defines  its  powers,  and  shows  the  method 
by  which  it  acquires  the  stock  of  its  ideas,  and 
accumulates  general  knowledge.* 

COMPOSITION. 

When  we  are  employed  after  a  proper  man- 
ner, in  the  study  of  composition,  we  are  culti- 
vating reason  itself.  True  rhetoric  and  sound 
logic  are  very  nearly  allied.  The  study  of  ar- 
ranging and  expressing  our  thoughts  with  pro- 
priety, teaches  us  to  think,  as  well  as  to  speak, 
accurately.  By  putting  our  sentiments  into 
words  we  always  conceive  them  more  distinctly. 
Every  one  who  has  the  slightest  acquaintance 
with  composition  knows,  that  when  he  ex- 
presses himself  ill  on  any  subject,  when  his 
arrangement  is  loose,  and  his  sentences  become 

*  Mr.  Kett's  Element*. 


COMPOSITION  323 

feeble,  the  defects  of  his  style  can,  almost  on 
every  occasion,  be  traced  back  to  his  indistinct 
conception  of  the  subject :  so  close  is  the  con- 
nection between  thoughts  and  the  words  in 
which  they  are  clothed.  The  study  of  com- 
position, important  in  itself  at  all  times,  has 
acquired  additional  importance  from  the  taste 
and  manners  of  the  present  age  ;  an  age  wherein 
improvements,  in  every  part  of  science,  have 
been  prosecuted  with  ardour.  To  all  the  libe- 
ral arts  much  attention  has  been  paid ;  and  to 
none  more  than  to  the  beauty  of  language,  and 
the  grace  and  elegance  of  every  kind  of  writing. 
The  public  ear  is  become  refined.  It  will  not 
easily  bear  what  is  slovenly  and  incorrect. 
Every  one  who  writes  must  aspire  to  some  merit 
in  expression,  as  well  as  in  sentiment,  if  he 
would  not  incur  the  danger  of  being  neglected 
and  despised.  I  will  not  deny  that  the  love  of 
minute  elegance,  and  attention  to  inferior  orna- 
ments of  composition,  may  have  engrossed  too 
great  a  degree  of  the  public  regard.  It  is  in- 
deed my  opinion,  that  we  lean  to  this  extreme ; 
often  more  careful  of  polished  style,  than  of 
storing  it  with  thought.  Yet  hence  arises  a 
new  reason  for  the  study  of  just  and  proper 
composition.  If  it  be  requisite  not  to  be  defi- 
28 


324  THE  YOUNG  MECHANIC. 

cient  in  elegance  and  ornament,  in  times  when 
they  are  in  such  high  estimation,  it  is  still  more 
requisite  to  attain  the  power  of  distinguishing 
false  ornament  from  true,  in  order  to  prevent 
our  being  carried  away  by  that  torrent  of  false 
and  frivolous  taste,  which  never  fails,  when  it 
is  prevalent,  to  sweep  along  with  it  the  raw  and 
the  ignorant.  They  who  have  never  studied 
eloquence  in  its  principles,  nor  have  been  trained 
to  attend  to  the  genuine  and  manly  beauties  of 
good  writing,  are  always  ready  to  be  caught  by 
the  mere  glare  of  language;  and  when  they 
come  to  speak  in  public,  or  to  compose,  have 
no  other  standard  on  which  to  form  themselves, 
except  what  chances  to  be  fashionable  and  po- 
pular, how  corrupted  soever  and  erroneous  that 
may  be.* 

Though  I  have  advised  the  pupil  to  exercise 
himself  in  composition,  yet  I  will  also  caution 
him  against  the  itch  of  scribbling.  Let  him 
never  take  the  pen  in  hand,  nor  place  the  paper 
before  him,  till  he  has  bestowed  much  time  and 
deep  thought  on  the  subject.  To  the  want  of 
this  previous  attention  we  owe  the  numerous 
productions  which  disgrace  letters,  and  which 
die  almost  as  soon  as  they  are  brought  forth ; 
*  l)r.  Blair's  Lectures. 


IMPROVEMENT  OF  MEMORY.  325 

which,  like  weeds  in  a  garden,  spring  up  luxu- 
riantly without  cultivation,  which  are  useless 
or  noisome,  and  which  only  serve  to  impede 
the  growth  of  salutary  plants  and  pleasant 
flowers.  Pretenders  arise  in  every  department, 
and  disgrace  it.  Let  the  liberal  and  solid  scholar 
attend  to  the  circumstances  of  time  and  place, 
in  the  modest  display  of  his  attainments.  It  is 
unmanly  timidity  to  conceal  them  on  proper 
occasions  ;  it  is  ridiculous  arrogance  to  intrude 
on  unwilling  and  injudicious  observers.  Mo- 
desty is  the  characteristic  of  real  merit;  and 
firmness,  of  conscious  dignity.  The  man  of 
sense  will  be  diffident,  but  at  the  same  time  will 
have  spirit  enough  to  repel  the  insolent  attacks 
of  ignorance  and  envy.*^ 

IMPROVEMENT  OF  THE  MEMORY. 

The  following  observations,  if  attended  to, 
may  greatly  assist  those  more  advanced  in  life, 
in  strengthening  the  memory.  1.  Let  the  stu- 
dent never  quit  any  branch  of  study  till  he  be 
perfectly  master  of  it,  and  can  comprehend  it 
as  a  whole;  as  well  as  in  parts.  2.  Endeavour 
to  link  and  connect  the  leading  ideas,  to  class 
facts,  and  arrange  them  under  different  heads ; 
*Dr  Knox. 


326  THE  YOUNG  MECHANIC.      • 

so  that  the  mind  shall  be  able  at  one  view  to 
recall  the  outlines  of  the  whole  science,  and  af- 
terwards to  pass  to  the  inferior  branches,  or  sub- 
divisions. The  ancients  formed  their  memories 
almost  entirely  by  this  method;  and  indeed 
memory  can  never  be  useful  without  svstem. 
3.  Never  commit  mere  words  to  memory  as 
substitutes  for  true  knowledge.  Many  a  young 
person  forgets  what  he  has  been  taught  because 
he  never  understood  it.  This  is  the  true  reason 
why  boys  make  so  wretched  a  proficiency  in 
attaining  the  Latin  language,  under  masters  who 
give  them  page  after  page  of  old  Lilly  to  com- 
mit to  memory,  without  the  occurrence  of  a 
question  or  an  explanation.  In  this  manner 
they  are  also  taught  their  catechisms,  the  ideas 
in  which  are  infinitely  above  their  comprehen- 
sion. 

The  first  thing  which  strikes  us,  in  looking 
over  Dr.  Franklin's  works,  is  the  variety  of  his 
observations  on  different  subjects.  We  might 
imagine,  that  a  very  tenacious  and  powerful 
memory  was  necessary  to  register  them;  but 
Dr.  Franklin  informs  us,  that  it  was  his  con- 
stant practice  to  note  down  every  thing  as  it 
occurred  to  him  :  he  urges  his  friends  to  do  the 
same ;  he  observes,  that  there  is  scarcely  a  day 


IMPROVEMENT  OF  MEMORY,  327 

passes  without  our  hearing  or  seeing  something, 
which,  if  properly  attended  to,  might  lead  to 
useful  discoveries.  By  thus  committing  his 
ideas  to  writing,  his  mind  was  left  at  liberty  to 
think.  No  extraordinary  effort  of  memory 
was,  even  on  the  greatest  occasions,  requisite.* 
On  the  whole,  the  most  effectual  way  to  ac- 
quire a  good  memory  is  by  constant  and  mo- 
derate exercises  of  it ;  for  the  memory,  like 
other  habits,  is  strengthened  and  improved  by 
daily  use.  It  is  scarcely  credible  to  what  a  de- 
gree both  active  and  passive  memory  may  be 
improved  by  long  practice.  Scaliger  reports 
of  himself  that  in  his  youth  he  could  repeat 
above  one  hundred  verses,  having  but  once 
read  them ;  and  Boethius  declares,  that  he  wrote 
his  comment  on  Claudian  without  consulting 
the  text.  The  extraordinary  memory  of  Ma- 
gliabechi  is  well  known.  That  of  Jediah  Bux- 
ton  was  of  a  peculiar  kind ;  so  long  was  it 
habituated  to  numbers,  that  it  could  fix  on 
nothing  else.  To  hope,  however,  for  such  de- 
grees of  memory  as  these,  would  be  equally 
vain  as  to  hope  for  the  strength  of  Hercules,  or 
the  swiftness  of  Achilles.  There  are  clergy-* 


*  Chiefly  by  Miss  Edgeworth. 

28* 


328  THE  YOUNG  MECHANIC. 

men  who  can  get  a  sermon  by  heart  in  two 
hours,  though  their  memory  when  they  began 
to  exercise  it,  was  rather  weak  than  strong  :  and 
pleaders,  with  other  orators,  who  can  speak  in 
public  extempore,  often  discover,  in  calling  in- 
stantly to  mind  all  the  knowledge  necessary  on 
the  present  occasion,  and  every  thing  of  im- 
portance which  may  have  been  advanced  in  the 
course  of  a  long  debate,  such  powers  of  reten- 
tion and  recollection  as,  to  the  man  who  has 
never  been  obliged  to  exert  himself  in  the  same 
manner,  are  altogether  astonishing.  As  habits, 
in  order  to  be  strong,  must  be  formed  in  early 
life,  the  memories  of  children  should  therefore 
be  constantly  exercised ;  but  to  oblige  them 
to  commit  to  memory  what  they  do  not  under- 
stand, prevents  their  faculties,  and  gives  them  a 
dislike  to  learning.  In  a  word,  those  who  have 
most  occasion  for  memory,  as  orators  and  pub- 
lic speakers,  should  not  suffer  it  to  lie  idle,  but 
constantly  employ  it  in  treasuring  up  and  fre- 
quently reviving  such  things  as  may  be  of  most 
importance  to  them ;  for  by  these  means,  it  will 
be  more  at  their  command,  and  they  may  place 
greater  confidence  in  it  on  any  emergency.* 

*  The  Idler. 


NATURAL  PHILOSOPHY.  329 

CHAPTER  XL 
THE  MECHANIC'S  STUDIES  CONTINUED. 

NATURAL  PHILOSOPHY  is  commonly  defined 
to  be  that  art  or  science  which  considers  the . 
powers  and  properties  of  natural  bodies,  and 
their  mutual  action  on  each  other.  Moral 
Philosophy  relates  to  whatever  concerns  the 
mind  and  intellect ;  Natural  Philosophy,  on  the 
other  hand,  is  only  concerned  with  the  material 
part  of  the  creation.  The  moralist's  business 
is  to  inquire  into  the  nature  of  virtue,  the 
causes  and  effects  of  vice,  to  propose  remedies 
for  it,  and  to  point  out  the  mode  of  attaining 
happiness.  The  naturalist,  on  the  contrary, 
has  nothing  to  do  with  spirit ;  his  business  is 
confined  to  body  or  matter.  The  first  and 
principal  part  of  this  science  is  to  collect  all  the 
manifest  and  sensible  appearances  of  things, 
and  reduce  them  into  a  body  of  Natural  History. 

Natural  Philosophy  differs  from  Natural 
History  in  its  appropriated  sense ,  the  business 
of  the  latter  is  only  to  observe  the  appearance 
of  natural  bodies  separately,  and  from  these 


330  THE  YOUNG  MECHANIC. 

appearances  to  class  them  with  other  bodies  to 
which  they  are  allied.  Natural  Philosophy 
goes  farther,  and  recites  the  action  of  two  or 
more  bodies  upon  each  other ;  and  though  it 
can  neither  investigate  nor  point  out  the  causes 
of  those  effects,  whatever  they  be,  yet  from 
mathematical  reasoning  combined  with  expe- 
rience, it  can  be  demonstrated,  that  in  such  cir- 
cumstances such  effects  must  always  take  place 

Natural  Philosophy,  till  lately,  has  been  di- 
vided into  four  parts,  commonly  called  the  foui 
branches,  viz. — 1.  Mechanics ;  2.  Hydrostatics  ; 
3.  Optics ;  and  4.  Astronomy ;  and  these  again 
subdivided  into  many  parts.  Modem  discove- 
ries have  added,  however,  two  more  parts,  viz., 
1.  Magnetism;  2.  Electricity  and  Galvanism. 
Every  one  is  acquainted  with  the  benefits  derived 
from  the  sciences  of  Mechanics,  Hydrostatics, 
and  Hydraulics,  to  which  we  are  indebted  for 
many  useful  inventions.  Among  these  are  wind 
and  water  mills,  aqueducts,  pumps,  fire  engines, 
steam  engines,  &c.,  &c. 

Pneumatics  supply,  even  to  a  superficial  en- 
quirer, much  instruction  and  amusement.  Sure- 
ly all  are  interested  in  the  nature  and  properties 
of  a  fluid  which  is  necessary  to  every  moment 
of  our  existence. 


NATURAL  PHILOSOPHY.  331 

How  great  would  have  been  the  surprise  of  the 
ancients,  could  they  have  conceived  the  effects? 
which  are  now  produced  by  the  reflection  and 
refraction  of  light  I     By  a  skilful  management 
of   these   properties,    telescopes,   and    various 
optical  instruments  are   constructed.     Objects 
too  remote  to  be  perceived  by  the  naked  eye, 
are  enlarged  and  rendered  visible.     The  satel- 
lites of  Jupiter  and  Saturn,  the  mountains  and 
cavities  in  the  moon,  and  the  changes  which 
take  place  on  the  sun's  disc,  are  thus  discover- 
ed, and  afford  subject  for  admiration  and  in- 
quiry.  Neither  is  the  delightful  scene  of  Optics 
confined  to  the  contemplation  of  distant  objects. 
Minute  animals,  the  vessels  of  plants,  and,  in 
short,  a  new  world  in  miniature  is  disclosed  to 
our  view  by  the  microscope,  and  an  inexhaus- 
tible fund  of  rational  entertainment  and  know- 
ledge is  brought  within  the  spere  of  our  senses. 
Of  all  the  sciences  to  which  geometry  im- 
parts the  solidity  of  its  principles,  and   the 
clearness  of  its  proofs,  the  most  beautiful  and 
the  most  sublime  is  Astronomy.     This  is  per- 
haps the  most  exact  and  most  definite  part  of 
natural  philosophy :  for  it  rectifies  the  errors 
of  sight,  with  respect  to  the  apparent  motions 
of  the  planets ;  explains  the  just  dimensions. 


332  THE  YOUNG  MECHANIC. 

relative  distances,  due  order,  and  exact  propor- 
tions of  the  spherical  bodies,  which  compose 
the  solar  system.  Nor  is  it  even  confined  to 
these  great  objects  of  nature,  since  it  opens  the 
stupendous  prospect  of  other  suns,  and  other 
systems  of  planets,  scattered  over  the  bound- 
less fields  of  space,  and  moving  in  obedience 
to  their  respective  laws.  It  marks  out  their 
particular  places,  assigns  their  various  names, 
and  classes  all  the  systems  of  worlds  in  their 
respective  constellations.  The  calculations  of 
astronomy  prove  the  certainty  of  the  future 
phenomena  of  the  heavenly  bodies,  when  the 
eccentric  comet  will  reappear,  after  having  tra- 
versed the  most  distant  regions  of  the  heavens, 
or  at  ^hat  point  of  time  the  bright  luminaries 
of  da^  and  night  will  be  immersed  in  the  par- 
tial, or  total  darkness  of  an  eclipse. 

CHEMISTRY. 

As  soon  as  man  begins  to  think,  and  to  rea- 
son, the  different  objects  which  surround  him 
on  all  sides  naturally  engage  his  attention. 
After  being  astonished  at  the  wonders  of  the 
atmospheric  and  higher  regions,  he  cannot  fail 
k)  be  struck  with  the  number,  diversity,  and 
beauty  of  those  on  earth,  and  naturally  feels  a 


CHEMISTRY  333 

desire  to  be  better  acquainted  with  their  proper- 
ties and  uses.  If  he  reflect  also,  that  he  him- 
self is  altogether  dependent  on  these  objects, 
not  merely  for  his  pleasures  and  comforts,  but 
for  his  very  existence,  this  desire  must  become 
irresistible.  Hence  that  curiosity,  that  eager 
thirst  for  knowledge,  which  animates  and  dis- 
tinguishes generous  minds. 

As  a  science,  chemistry  is  intimately  con- 
nected with  all  the  phenomena  of  nature  j  the 
causes  of  rain,  snow,  hail,  dew,  wind,  earth- 
quakes ;  even  the  changes  of  the  seasons  can 
never  be  explored  with  any  chance  of  success 
while  we  are  ignorant  of  chemistry  :  and  the 
vegetation  of  plants,  and  some  of  the  most  im- 
portant functions  of  animals,  have  received  all 
their  illustration  from  the  same  source'.  No 
study  can  give  us  more  exalted  ideas  of  the 
wisdom  and  goodness  of  the  eternal  cause  than 
this.  As  an  art,  it  is  intimately  connected  with 
all  our  manufactures :  the  glass-blower,  the 
potter,  the  smith,  and  every  other  worker  in 
metals ;  the  tanner,  the  soap-maker,  the  dyer, 
the  bleacher,  are  practical  chemists ;  and  the 
most  essential  improvements  have  been  intro- 
duced into  all  these  arts  by  the  progress  which 
chemistry  has  made  as  a  science.  Agriculture 


334  THE  YOUNG  MECHANIC. 

can  only  be  improved  rationally,  and  certainly, 
by  calling  in  the  assistance  of  chemistry ;  and 
the  advantages  which  medicine  has  derived 
from  the  same  source,  are  too  obvious  to  be 
pointed  out.* 

NATURAL  HISTORY. 

I  am  convinced,  says  Rousseau,  that  at  all 
times  of  life,  the  study  of  nature  abates  the 
taste  for  frivolous  amusements,  prevents  the 
tumult  of  the  passions,  and  provides  the  mind 
with  a  nourishment  which  is  salutary,  by  filling 
it  with  objects  most  worthy  of  its  contempla 
tion. 

Of  all  the  studies  in  which  the  minds  o? 
youth  may  be  employed,  none,  perhaps,  deserve 
more  strongly  to  be  recommended,  than  thos* 
of  natural  history  and  physics.  The  object* 
on  which  they  are  occupied  being  such  as  com* 
under  the  Cognizance  of  our  senses,  they  ar«s 
more  easily  comprehended  by  the  juvenile  un 
derstanding,  than  the  refinements  of  grammar 
or  the  abstract  ideas  of  moral  philosophy:  p- 
the  same  time,  they  afford  an  inexhaustible  fun^ 
of  entertainment;  and  their  great  utility  ir 

*  Thomson's  Chemistry. 


NATURAL  HISTORY.  333 

rvery  situation  in  life  is  universally  acknow- 
ledged.* 

It  is  the  glorious  privilege  of  man,  while 
other  animals  are  confined  within  the  limits 
which  instinct  has  prescribed,  to  carry  his  ob- 
servations beyond  his  own  immediate  wants, 
and  to  contemplate  the  universe  at  large.  He 
extends  his  inquiries  to  all  the  objects  which 
surround  him  ;  exercises  his  judgment,  and  in- 
forms his  understanding,  by  ascertaining  their 
na&nre,  properties,  and  uses.  In  the  various 
branches  of  mathematics,  in  the  abstract  specu- 
lations of  metaphysics,  or  in  searching  the  re- 
cords of  history,  he  is  solely  intent  on  the  opera- 
tions of  his  own  mind,  or  the  actions  of  him- 
self and  his  fellow  creatures :  but  in  the  study 
of  nature,  he  examines  every  object  presented 
to  his  senses,  and  takes  a  general  survey  of  the 
wide  and  interesting  prospect  of  the  creation. 
The  earth  he  treads,  the  ocean  he  crosses,  the 
air  he  breathes,  the  starry  heavens  on  which  he 
gazes,  the  mines  and  caverns  he  explores,  all 
present  to  him  abundant  materials  for  his  re- 
searches. And,  when  thus  employed,  he  is 
engaged  in  a  manner  peculiarly  suitable  to  his 

*  Preface  to  Pleasing  Preceptor. 

29 


33n  THE  YOUNG  MECHANIC. 

faculties,  since  he  alone  is  capable  of  know- 
ledge, he  alone  is  distinguished  by  the  power 
of  admiration,  and  exalted  by  the  faculty  of 
reason.  The  terraqueous  globe  presents  a  most 
glorious  and  most  sublime  prospect,  equally 
worthy  of  the  capacity  of  man  to  contemplate, 
and  beautiful  to  his  eye  to  behold.  And  the 
treasures  of  nature,  which  this  prospect  com- 
prehends, are  so  rich  and  inexhaustible,  that 
they  may  furnish  employment  for  his  greatest  di- 
ligence, stimulated  by  the  most  ardent  curiosity 
and  assisted  by  the  most  favourable  opportuni- 
ties. At  the  same  time  that  she  solicits  him  to 
follow  her,  not  only  in  her  open  walks,  but 
likewise  to  explore  her  secret  recesses,  she  fails 
not  to  reward  him  with  the  purest  gratifications 
of  the  mind,  because  at  every  step  he  takes, 
new  instances  of  beauty,  variety,  and  perfection 
are  unfolded  to  his  view. 

The  study  of  the  works  of  nature  is  in  itself 
capable  of  affording  the  most  refined  pleasure, 
and  the  most  edifying  instruction.  All  the  ob- 
jects with  which  we  are  surrounded,  the  small- 
est as  well  as  the  greatest,  teach  us  some  useful 
lesson.  All  of  them  speak  a  language  directed 
to  man,  and  to  man  alone.  Their  evident  ten- 
dency to  some  determined  end,  marks  the  de- 


NATURAL  HISTORY.  337 

sign  of  a  great  Creator.  The  volume  of  crea- 
tion contains  the  objects  of  arts,  science,  and 
philosophy,  and  is  open  to  the  inspection  of  all 
the  inhabitants  of  the  globe.  Nature  speaks 
by  her  works  an  universal  language,  the  rudi- 
ments of  which  are  peculiarly  adapted  to  the 
inclination  and  capacity  of  the  young,  whose 
curiosity  may  be  gratified  and  excited  by  turns  ; 
but  more  profound  and  extensive  inquiries  are 
suitable  to  the  contemplation  of  persons  of 
every  age ;  and  no  subjects  can  be  more  worthy 
of  their  attentive  observation.* 

A  walk  in  the  fields,  after  reading  a  little  in 
natural  history,  may  furnish  opportunities  of 
important  instruction.  The  hills,  the  dales,  and 
quarries  afford  matter  of  speculation  on  their 
formation,  use,  and  beauty.  And  this  may  be 
rendered  intelligible  to  a  child,  by  a  person 
who  really  understands  the  subject,  and  is  not 
a  mere  pedant  who  has  only  committed  techni- 
cal words  to  memory.  So  in  all  probability 
may  every  branch  of  real  knowledge.  Those 
branches  which  are  now  lost  to  common  sense 
by  calculations  and  mathematical  processes,  are 
not  always,  if  they  be  ever  understood  by  those 

*  Mr.  Kett's  Elements. 


338  THE  YOUNG  MECHANIC. 

who  profess  to  understand  them.  Every  thing 
which  is  not  applicable  to  use,  and  the  applica- 
tion of  which  cannot  be  made  obvious  to  com- 
mon sense,  is  gothic  jargon,  and  not  science ; 
and  people  who  glory  in  such  acquisitions  have 
not  a  clear  and  good  idea  of  what  constitutes 
real  knowledge.  This  explains  the  problem, 
why,  in  the  present  state  of  learning,  there  are 
no  plain,  intelligible,  and  easy  methods  of  teach- 
ing the  sciences,  and  so  few  good  elementary 
books.  The  reason  is,  that  the  sciences  are 
not  generally  and  thoroughly  understood.  Every 
man  can  easily  teach  another  what  he  perfectly 
understands  himself.  But  if  half  his  terms  be 
merely  technical,  and  he  can  give  no  definitions 
of  them  which  convey  ideas,  it  is  no  wonder 
that  learning  is  difficult,  as  it  is  always  painful 
to  commit  to  memory  words  which  have  no 
meaning ;  and  all  the  progress  made  upon  such 
foundations  is  ever  attended  with  that  anxiety 
and  anguish,  which  have  so  strongly  marked 
the  countenances  of  our  philosophers.  In  the 
same  manner  as  the  general  truths  of  natural 
history  might  be  occasionally  exemplified  in 
the  fields,  many  of  the  mathematic,  astronomic, 
and  particularly  the  mechanic  problems,  rnigh* 
be  examined  in  a  walk.  This  would  not  only 


XATURAL  HISTORY. 

6e  ^esent  instruction,  but  bring  the  pupil  into 
a  habit  of  having  an  object  and  a  view  in  every 
action.  He  would  not  then  experience  the 
common  unhappiness  of  not  knowing  what  to 
do  with  himself;  or  when  he  has  determined 
on  a  walk  or  a  ride,  be  miserable  for  want  of 
being  able  to  determine  where  to  gv  or  with 
what  object  to  engage  his  thoughts  * 


340  THE  YOUNG  MECHANIC. 

CHAPTER  XII. 
THE  MECHANIC'S  STUDIES  CONTINUED 

HISTORY. 

• 

CURIOSITY  is  one  of  the  strongest  and  most 
active  principles  of  human  nature.  Through- 
out the  successive  stages  of  life,  it  seeks  with 
avidity  for  those  gratifications,  which  are  con- 
genial with  the  different  faculties  of  the  mind. 
The  child,  as  soon  as  the  imagination  begins  to 
open,  eagerly  listens  to  the  tales  of  his  nurse : 
the  youth,  at  a  time  of  life,  when  the  love  of 
what  is  new  and  uncommon  is  quickened  by 
sensibility,  is  enchanted  by  the  magic  of  ro- 
mances and  novels :  the  man,  whose  mature 
judgment  inclines  him  to  the  pursuit  of  truth, 
applies  to  genuine  history,  which  even  in  old 
age  continues  to  be  a  favourite  object  of  his  at- 
tention ;  since  his  desire  to  be  acquainted  with 
the  transactions  of  others  has  nearly  an  equal 
power  over  his  mind  with  the  propensity  to 
relate  what  has  happened  to  himself 

History,  considered  with  respect  to  the  nature 
of  its  subjects,  may  be  divided  kito  general  and 


HISTORY.  34] 

particular ;  and  with  respect  to  time,  into  an- 
cient and  modern.  Ancient  history  commences 
with  the  creation,  and  extends  to  the  reign  of 
Charlemagne,  in  the  year  of  our  Lord  800. 
Modern  history,  beginning  with  that  period, 
reaches  down  to  the  present  times.  General 
history  relates  to  nations  and  public  affairs,  and 
may  be  subdivided  into  sacred,  ecclesiastical, 
and  profane.  Biography,  memoirs,  and  letters, 
constitute  particular  history.  Statistics  refer  to 
the  present  condition  of  nations.  Geography 
and  Chronology  are  important  aids,  and  give 
order,  regularity  and  clearness  to  them  all. 

To  draw  the  line  of  proper  distinction  be- 
tween authentic  and  fabulous  history,  is  the 
first  object  of  the  discerning  reader.  Let  him 
not  burden  his  memory  with  events  which 
ought  perhaps  to  pass  for  fables ;  let  him  not 
fatigue  his  attention  with  the  progress  of  em- 
pires, or  the  succession  of  kings,  which  are 
thrown  back  into  the  remotest  ages.  He  will 
find  that  little  dependence  is  to  be  placed  upon 
the  relations  of  those  affairs  in  the  Pagan 
world,  which  precede  the  invention  of  letters, 
and  were  built  upon  mere  oral  tradition.  Let 
him  leave  the  dynasties  of  the  Egyptian  kings, 
the  expeditions  of  Sesostris, Bacchus,  and  Jason, 


342  THE  YOUNG  MECHANIC. 

and  the  exploits  of  Hercules  and  Theseus,  for 
poets  to  embellish,  or  chronologists  to  arrange. 
The  fabulous  accounts  of  these  heroes  of  anti- 
quity may  remind  him  of  the  sandy  deserts, 
lofty  mountains,  and  frozen  oceans,  which  are 
laid  down  in  the  maps  of  the  ancient  geogra- 
phers, to  conceal  their  ignorance  of  remote 
countries.  Let  him  hasten  to  firm  ground, 
where  he  may  safely  stand,  and  behold  the 
striking  events,  and  memorable  actions,  which 
the  light  of  authentic  records  display  to  his 
view.  They  alone  are  amply  sufficient  to  en- 
rich his  memory,  and  to  point  out  to  him  well 
attested  examples  of  all  that  is  magnanimous, 
as  well  as  of  ail  that  is  vile  ;  of  all  that  debases, 
and  all  that  ennobles  mankind.* 

Unfortunately  the  study  of  history  is  not 
without  its  dangers  and  inconveniences  of  va- 
rious kinds.  It  is  a  very  difficult  matter  to 
place  one's  self  in  such  a  point  of  view  as  to 
be  able  to  judge  equitably  of  our  fellow  crea- 
tures. It  is  one  of  the  common  vices  of  his- 
tory to  paint  man  in  a  disadvantageous  rather 
than  in  a  favourable  light.  Revolutions  and 
fatal  catastrophes  being  most  interesting,  so  long 
as  a  people  have  continued  to  increase  and 
*  Mr.  Kelt's  Elements. 


HISTORY  343 

prosper  in  the  calm  of  a  peaceable  government 
history  has  remained  silent ;  it  speaks  of  na- 
tions only  when,  growing  insupportable  to 
themselves,  they  begin  to  interfere  with  their 
neighbours,  or  to  suffer  their  neighbours  to  in- 
terfere with  them.  We  are  favoured  with  very 
exact  accounts  of  those  nations  which  verge 
towards  destruction ;  but  of  those  which  have 
been  flourishing,  we  have  no  history;  they 
have  been  so  wise  and  happy  as  to  furnish  no 
events  worth  recording.  The  historical  rela- 
tions of  facts  which  we  meet  with,  are  by  no 
means  accurate  delineations  ;  they  change  their 
aspect  in  the  brain  of  the  historian,  they  bend 
to  his  interest,  and  are  tinctured  by  his  preju- 
dices. What  historian  ever  brought  his  reader 
to  the  scene  of  action,  and  laid  the  event  cir 
cumstantially  as  it  happened  ?  Ignorance  and 
partiality  disguise  every  thing.  How  easy  it  is 
to  give  a  thousand  varied  appearances  to  the 
same  facts,  merely  by  a  difference  in  the  repre- 
sentation of  circumstances.  Exhibit  an  object 
in  different  points  of  view,  and  we  scarcely  be- 
lieve it  to  be  the  same,  and  yet  nothing  is 
changed,  except  the  eye  of  the  spectator.,  How 
often  has  it  happened  that  a  few  trees,  a  hill  on 
the  right  or  left,  or  a  sudden  cloud  of  dust, 


344  THE  YOUNG  MECHANIC. 

have  turned  the  scale  of  victory,  without  the 
cause  first  being  perceived  ?  Nevertheless  the 
historian  will  assign  a  reason  for  the  victory  or 
defeat  with  as  much  confidence  as  if  he  had 
been  at  the  same  instant  in  every  part  of  the 
battle.  The  worst  historians,  for  a  young 
reader,  are  those  who  favour  us  with  their  judg- 
ment. A  plain  narrative  of  facts  is  all  he  wants  : 
let  him  judge  for  himself,  and  he  will  learn  to 
know  mankind.  If  he  be  constantly  guided  by 
an  author's  opinion,  he  sees  only  with  the  eyes 
of  another;  and  when  these  are  taken  from 
him  he  does  not  see  at  all.  History  is  generally 
defective  in  recording  only  those  facts  which 
are  rendered  conspicuous  by  name,  place,  or 
date ;  but  the  slow  progressive  causes  of  those 
facts,  not  being  thus  distinguished,  remain  for 
ever  unknown.  A  madness  for  party  having 
possession  of  them  all,  they  never  endeavour 
to  see  things  as  they  really  are,  but  as  they 
best  agree  with  their  favourite  hypotheses.* 

It  is  the  business  of  history  to  distinguish 
between  the  miraculous  and  marvellous;  to 
reject  the  first  in  all  narrations  merely  profane 
and  human  ;  to  scruple  the  second ;  and  when 

*  Rousseau,  b.  iv. 


HISTORY.  345 

obliged  by  undoubted  testimony  to  admit  of 
something  extraordinary,  to  receive  as  little  ot 
it  as  is  consistent  with  the  known  facts  and 
circumstances.* 

In  undertaking  a  course  of  history,  it  is  cer- 
tainly of  great  advantage  to  follow  the  chrono- 
logical order  of  events.  You  have  then  the 
gradual  progress  of  man  from  barbarism  to 
refinement;  from  refinement  to  corruption,  ve- 
nality, and  slavery  ;  from  slavery  back  again  to 
darkness  and  ignorance ;  and  from  this  state 
again  to  knowledge,  civilization,  and  liberty. 
The  most  ancient  history,  except  the  Bible,  is 
Herodotus ;  and  no  history  was  ever  more  de- 
lightful for  its  simplicity,  perspicuity,  the  un- 
affected style  of  the  narrative,  and  easy  and 
harmonious  flow  of  the  language.  Mr.  Beloe's 
translation,  though  not  elegant,  partakes  in  some 
measure,  of  the  simplicity  of  the  original.  The 
history  of  Thucydides  takes  not  so  wide  a 
scope  as  that  of  Herodotus,  but  the  period 
which  he  describes  is  interesting,  and  his  man- 
ner is  incomparable.  Smith's  translation  is 
tolerably  good,  and  even  that  of  Hobbes  may 
be  read  without  disgust.  A  more  connected 

*Hume. 


346  THE  YOUNG  MECHANIC 

view  of  ancient  history  may  be  learnt  from 
Rollin.  The  Ancient  Universal  History  is  an 
excellent  and  elaborate  compilation,  but  it  is 
tedious,  and  the  style  is  dry  and  inharmonious  : 
it  is  a  book  therefore  rather  for  reference  than 
study.  The  indefatigable  Dr.  Mavor  has  pro- 
duced an  abridgment  of  this  work,  with  addi 
tions,  to  the  year  1802,  in  25  volumes,  18mo 
Of  the  Roman  historians  there  is  a  deplorable 
dearth  of  good  translations.  The  order  in 
which  they  may  be  read  is  Livy,  Sallust,  Ca3sar. 
The  Epistles  of  Cicero  are  chiefly  historical, 
which  are  admirably  translated  by  Mr.  Mel- 
moth.  Plutarch's  Lives  should  be  read  imme- 
diately after  the  Greek  and  Latin  historians,  or 
rather  in  conjunction  with  them  :  a  good  trans- 
lation has  been  done  by  the  brothers  Lang- 
horne.  Of  modern  works,  Vertot's  Roman 
Revolutions,  Montesquieu's  Greatness  and  De- 
cline of  the  Romans,  and  Dr.  Middleton's  in- 
comparable Life  of  Cicero,  may  be  read  with 
the  ancient  historians.  The  last  is  a  produc- 
tion of  original  genius,  and  yet  comprises  all 
which  is  most  excellent  in  the  writings  of  the 
great  man  whose  life  it  narrates.  The  Anabasis 
of  Xenophon,  and  the  history  of  Polybius  are 
most  interesting  and  engaging  books ;  of  the 


HISTORY.  347 

latter  there  is  a  translation  by  Hampton.  Of 
the  English  compilations  which  contain  the 
history  of  the  Roman  commonwealth,  Fergu- 
son's is  preferable  to  Hook's.  Suetonius's  His- 
tory of  the  Twelve  Caesars  is  an  ill-written 
book,  yet  it  contains  facts  which  are  not  to  be 
found  in  any  other  original  author.  Tacitus  is 
a  treasure,  not  merely  on  account  of  the  his- 
torical matter  which  it  contains,  but  for  the 
mass  of  moral  instruction  which  it  conveys. 
Murphy's  translation  may  be  pronounced  supe- 
rior to  Gordon's.  After  finishing  Tacitus,  we 
must,  of  necessity,  have  recourse  to  compila- 
tion. Mr.  Gibbon  takes  up  the  subject  where 
Tacitus  left  it,  and  certainly  a  nobler  monu- 
ment of  genius  was  never  erected,  than  the 
"  Decline  and  Fall  of  the  Roman  Empire ;"  a 
narrative  which  extends  to  so  modern  a  period, 
that  a  few  books  will  serve  to  unite  the  chain 
of  history  with  that  of  our  own  country.  Dr. 
Robertson's  Charles  the  Fifth  is  perhaps  the 
most  perfect  historical  composition  in  the  En- 
glish language ;  and  Dr.  Watson's  history  is 
well  connected  with  it ;  both  of  which  relate 
to  some  of  the  most  important  events  recorded 
in  history,  the  reformation  of  religion,  and  the 
establishment  of  the  Batavian  republic.  Mr. 
30 


348  THE  YOUNG  MECHANIC 

Wraxall  has  filled  up  a  chasm  on  the  historical 
shelf,  by  his  agreeable  history  of  France  •  yet 
the  student  should  not  satisfy  himself  with  that 
author's  account  of  the  age  of  Henry  the  Great, 
but  inspect  for  himself  the  interesting  and  un- 
blemished pages  of  Sully ;  and  there  are  few 
scholars  who  will  not  find  exquisite  pleasure  in 
the  general  history  of  the  correct  De  Thou. 
Vertot's  Revolutions  of  Sweden  and  of  Portu- 
gal, are  both  of  them  animated  narratives  of 
important  events.  Voltaire's  Age  of  Louis  the 
fourteenth  and  fifteenth,  may  be  classed  among 
original  histories,  though  not  of  the  first  rank ; 
his  Charles  the  Twelfth  borders  much  on  the 
romance.  Dr.  Robertson's  History  of  Ameiica 
is  a  much  admired  composition.  After  such  a 
course  of  reading,  the  student  will  not  be  ill 
prepared  for  the  history  of  his  own  country. 
Hume's  History  is  a  bad  compilation.  Hume 
is,  moreover,  the  avowed  enemy  of  the  two 
principles  which  conduce;  most  to  ihe  happiness 
of  mankind,  ^eligion  ana  liberty;  and  he  who 
makes  him  t'ue  fciandard  of  his  historical  faith, 
will  embrace  numerous  errors,  arising  not 
merely  trom  design  but  from  negligence.  As  a 
general  history,  Rapin's  is  preferable ;  and  if 
the  state  papers  be  passed  over,  it  will  not  be 


HISTORY.  349 

'bund  more  voluminous  than  Hume.  Perhaps 
a  better  course  of  English  historical  reading 
would  be  to  take  Dr.  Henry's  History  for  the 
early  periods ;  from  the  conclusion  of  which 
he  may  proceed  with  Rapin  to  the  date  of  Cla- 
rendon's History ;  and,  for  the  affairs  of  Scot- 
land, having  recourse  to  the  classical  narrative 
of  George  Buchannan,  and  the  elegant  history 
of  Queen  Mary,  by  the  accomplished  Robert- 
son. Clarendon's  History,  with  his  life,  are 
invaluable  records ;  but  his  statements  will,  in 
some  instances,  be  corrected  by  Whitlock's 
Memorials,  which  every  student  of  history 
ought  to  read,  and  by  the  plain  and  manly,  but 
interesting  Memoirs  of  the  ill-treated  Ludlow. 
Though  Bishop  Burnet's  egotisms  have  been 
ridiculed  by  Pope,  Arbuthnot  and  Swift,  yet  he 
will  continue  to  be  read  by  every  one  who 
wishes  to  inform  himself  correctly  of  the  man- 
ners and  circumstances  of  the  times  in  which 
that  excellent  prelate  and  really  candid  writer 
lived.  Mrs.  Macaulay's  history  evidently  fa- 
vours republicanism,  but  her  narrative  is  pure, 
and  she  is  scrupulously  exact  in  producing  evi- 
dence and  authority  for  all  her  facts. 

The  student  of  history  should  always  read 
with  a  map  of  the  country  before  him.    A  good 


350  THE  YOUNG  MECHANIC. 

Biographical  Dictionary  is  also  an  useful  com- 
panion in  the  study  of  history.  Various  plans 
have  been  recommended  for  connecting  history 
with  chronology  in  the  mind ;  the  best  method 
is  perhaps  to  endeavour  to  fix  in  the  memory 
the  dates  of  some  of  the  most  remarkable  events. 
The  intermediate  transactions  will  generally  be 
found  to  have  some  link  of  association  with 
the  great  events,  and  it  will  not  be  difficult  to 
decide  nearly  on  the  date  of  any  of  them. 
There  is,  however,  no  better  aid  to  the  memo- 
ry than  Dr.  Priestley's  Historical  Chart.* 

On  English  History,  the  late  Earl  of  Chatham 
thus  wrote  to  his  nephew.  tt  If  you  have 
finished  the  abridgment  of  English  History 
and  of  Burnet's  History  of  the  Reformation,  I 
recommend  to  you  next,  before  any  other  read- 
ing of  history,  Oldcas tie's  Remarks  on  the  His- 
tory of  England,  by  Lord  Bolingbroke.  Let 
me  apprise  you  of  one  thing  before  you  read 
them,  and  that  is,  that  the  author  has  bent  some 
passages  to  make  them  invidious  parallels  to 
the  times  he  wrote  in;  therefore  be  aware  of 
that,  and  depend,  in  general,  on  finding  the 
truest  constitutional  doctrines;  and  that  the 

*  Mon.  Mag.  May,  1797. 


HISTORY.  351 

facts  of  history,  though  warped,  are  no  where 
falsified.  I  also  recommend  Nathaniel  Bacon's 
Historical  and  Political  Observations ;  it  is 
without  exception,  the  best  and  most  instruc- 
tive book  we  have  on  matters  of  that  kind 
They  are  both  to  be  read  with  attention,  and 
twice  over ;  Oldcastle  s  Remarks  to  be  studied 
and  almost  got  by  heart,  for  the  inimitable 
beauty  of  the  style,  as  well  as  the  matter.  Ba- 
con for  the  matter  chiefly,  the  style  being  un- 
couth, but  the  expression  forcible  and  striking. 

"  I  desired  you  sometime  since  to  read  Cla- 
rendon's History  of  the  Civil  Wars.  I  have 
lately  read  a  much  honester  and  more  instruc- 
tive book,  of  the  same  period  of  history ;  it  is 
the  History  of  the  Parliament,  by  Thomas 
May,  Esq.  If  you  have  not  read  Burnet's  His- 
tory of  his  Own  Times,  1  beg  you  will. 

"  I  suppose  you  are  going  through  the  bio- 
graphers, from  Edward  the  Fourth  downwards, 
nor  intending  to  stop  till  you  reach  to  the  con- 
tinuator  of  honest  Kapin.  There  is  a  little 
book  which  1  never  mentioned,  Welwood's  Me- 
moirs ;  I  recommend  it.  Davis's  Ireland  must 
not  on  any  account  be  omitted ;  it  is  a  great 
performance,  a  masterly  work,  and  contains 
much  depth  and  extensive  knowledge  in  state 


352  THE  YOUNG  MECHANIC. 

matters,  and  settling  of  countries,  in  a  very 
short  compass.  I  have  met  with  a  scheme  of 
chronology  by  Blair,  showing  all  contemporary 
historical  characters,  through  all  ages :  it  is  of 
great  use  to  consult  frequently,  in  order  to  fix 
periods,  and  throw  collateral  light  upon  any 
particular  branch  you  are  reading.^* 

Such  is  the  recommendation  of  { Chatham,  a 
first  rate  authority. 

Among  the  historical  works  produced  in  our 
own  country,  Bancroft's  History  of  the  United 
States,  3  vols.  8vo.,  is  entertaining  and  carefully 
written ;  but  it  only  brings  the  history  down  to  a 
period  shortly  before  the  commencement  of  the 
Revolution.  Frost's  History  of  the  United 
States,  written  for  schools,  brings  it  down  to 
the  year  1836.  Prescott's  Ferdinand  and  Isa- 
bella, and  Irving's  Columbus  are  delightful  to 
read,  and  of  the  highest  authority. 

BIOGRAPHY. 

Biography*  is  a  highly  important  branch  of 
history.  The  biographer,  by  his  accurate  re- 
searches, supplies  the  deficiencies  of  the  histo- 
rian. What  the  latter  gives  us  only  in  outlines 

•  Letters,  passim. 


BIOGRAPHY.  353 

and  sketches,  the  former  presents  in  more  com- 
plete and  highly  finished  portraits.  Their  pro- 
vince does  not  merely  extend  to  those  who 
have  acted  upon  the  great  theatre  of  the  world, 
as  sovereigns,  statesmen,  and  warriors  ;  but  to 
all  who  have  improved  human  life  by  their 
useful  discoveries,  adorned  it  by  their  works 
of  genius,  and  edified  mankind  by  their  exam- 
ples. With  what  pleasure  do  we  select  a  Ba- 
con, a  Boyle,  a  Newton,  an  Addison,  a  Locke, 
a  Radcliffe,  a  Howard  and  a  Hanway,  from  the 
multitudes  which  surround  them,  and  become 
acquainted  with  their  particular  characters  and 
conduct !  To  contemplate  such  men,  not  in- 
flamed by  vain  ambition,  or  courting  empty 
popularity,  but  seeking  retirement,  and  giving 
dignity  to  the  walks  of  private  life  by  the  efforts 
of  genius,  and  the  exertions  of  philanthropy, 
is  a  high  gratification  to  the  mind,  and  inspires 
it  with  an  admiration  and  a  love  of  those  vir- 
tues, which  come  within  the  reach  of  general 
imitation. 

No  species  of  writing  gives  a  more  perfect 
insight  into  the  minds  of  men,  than  their  let- 
ters. We  observe  them  as  they  thought  in  their 
retired  moments,  when,  withdrawn  from  the 
bustle  of  the  world,  they  aave  free  scope  to 


35  i  THE  YOUNG  MECHANIC. 

their  unrestrained  opinions,  and  poured  them 
without  reserve,  into  the  bosom  of  their  friends. 
Among  the  numerous  instances,  which  might 
hr  selected  of  epistolary  excellence,  we  distin- 
guish the  letters  of  Cicero,  which  display  the 
sentiments  of  a  vigorous  mind,  and  give  an  in- 
sight into  the  eminent  characters  of  his  event- 
ful times.  Pliny,  in  letters  remarkable  for  neat- 
ness and  precision  of  thought,  expresses  the 
dictates  of  a  cultivated  and  generous  mind.  If 
we  turn  our  attention  to  the  epistolary  litera- 
ture of  our  own  country,  we  shall  find  that  the 
piety  and  affection  of  Lady  Russel,  the  quaint- 
ness  and  pleasantry  of  Howel,  the  manliness 
and  political  sagacity  of  Stafford,  the  philoso- 
phical exactness  and  cool  judgment  of  Locke, 
the  simplicity  of  Rundle,  the  moralizing  vein 
of  Johnson,  and  the  taste  and  elegance  of  Gray, 
mark  their  respective  letters  with  the  strongest 
characters  of  originality,  and  give  us  the  most 
pleasing  pictures  of  their  minds.* 

Besides  the  names  above  enumerated  by  Mr. 
Kett,  the  following  may  be  added,  as  justly 
celebrated  letter  writers,  viz. :  Pope,  Swift,  Ad 
dison,  Steele,  Arbuthnot,  Gay,  Shenstone,  Sterne, 

*  Mr.  Kett's  Elements. 


BIOGRAPHY.  355 

Lyttleton,  Lady  Mary  Wortley  Montague,  Rich- 
ardson, Chesterfield,  Cowper,  Sevigny,  Mainte- 
non,  Burns,  Lord  Byron,  and  Horace  Walpole. 
Biography  is,  in  general,  a  most  pleasing  as 
well  as  instructive  branch  of  literature.  When 
faithfully  written  it  unveils  man  to  man ;  dis- 
covers the  virtues  and  vices,  the  nobleness  and 
meanness  of  which  he  is  capable ;  and  shows 
how  the  original  sameness  of  human  nature  is 
varied  by  the  operation  of  external  causes  into 
ten  thousand  different  shapes,  and  assumes  as 
many  shades  and  hues.  Man,  to  be  known, 
must  be  viewed  in  every  situation ;  and  when- 
ever he  is  fairly  exhibited,  whatever  may  have 
been  his  rank,  station,  or  circumstances  of  birth 
or  fortune,  a  valuable  addition  is  made  to  sci- 
ence. Whether  the  record  respects  the  strug- 
gles of  talents  and  worth  through  the  chilling 
regions  of  obscurity  and  penury,  up  to  the 
glittering  eminences  of  fame  and  reward ;  or 
whether  it  details  the  operations  of  pride  and 
ambition  on  minds  born  to  wealth  and  power ; 
it  presents  an  useful  lesson,  which  those  who 
are  disposed  to  exertion  and  virtue  will  not 
read  in  vain.* 


*  Mon.  Rev. 
30* 


358  THE  YOUNG  MECHANIC. 

J  would  begin  the  study  of  the  human  heart, 
says  Rousseau,  by  reading  the  lives  of  particu- 
lar men ;  for  there  the  hero  conceals  not  him- 
self for  a  moment.  The  biographer  pursues 
him  into  the  most  secret  recesses,  and  exposes 
him  to  the  piercing  eye  of  the  spectator ;  he  is 
best  known  when  he  believes  himself  most 
concealed.  I  confess  the  genius  of  a  people  is 
very  different  from  that  of  man  considered  as 
an  individual,  and  that  we  shall  be  imperfectly 
acquainted  with  mankind  if'  we  neglect  the 
study  of  the  multitude  ;  but  it  is  also  true,  that 
we  must  begin  by  studying  man  in  order  to 
know  mankind ;  and  that  if  we  know  the  pro- 
pensities of  each  individual  it  will  not  be  diffi- 
cult to  foresee  their  effects  when  combined  in 
the  body  of  the  people.  The  lives  of  kings 
may  be  written  and  rewritten,  but  we  shall 
never  see  another  Suetonius.  Plutarch's  excel- 
lence consists  chiefly  in  those  very  minutia3 
into  which  we  dare  not  enter.  There  is  an 
inimitable  gracefulness  in  his  manner  of  paint- 
ing great  men  engaged  in  trivial  employments, 
and  he  is  so  happy  in  the  choice  of  his  inci- 
dents, that  frequently  a  single  word,  a  smile,  a 
gesture,  is-  sufficient  to  characterize  his  hero. 
Marshal  Turenne  was  incontestably  one  of  the 


BIOGRAPHY.  357 

greatest  men  of  the  age  in  which  he  lived.  The 
writer  of  his  life  has  had  the  resolution  to  ren- 
der it  interesting  by  relating  some  minute  par- 
ticulars which  make  his  hero  known  and  be- 
loved ;  but  how  many  was  he  obliged  to  sup- 
press, which  would  have  taught  us  to  know 
and  love  him  still  more!  I  shall  instance  one 
which  I  had  from  good  authority,  and  which 
Plutarch  would  by  no  means  have  omitted,  but 
which  Ramsay,  if  he  had  known  it,  would  not 
have  dared  to  relate.  The  Marshal  happened, 
one  hot  day,  to  be  looking  out  at  the  window 
of  his  antichamber  in  a  white  waistcoat  and 
night  cap.  A  servant  entering  the  room,  was 
deceived  by  his  dress,  and  mistook  him  for  one 
of  his  under  cooks.  He  crept  softly  behind 
him,  and  gave  him  a  violent  slap  on  the  breech. 
The  Marshal  instantly  turned  about,  and  the 
fellow,  frightened  out  of  his  senses,  beheld  the 
face  of  his  master :  down  he  fell  on  his  knees. 
"  Oh !  my  lord !  I  thought  it  was  George !" 
"  And  suppose  it  had  been  George,*5  replied 
the  Marshal,  rubbing  his  back,  "  you  ought 
«ot  to  have  struck  quite  so  hard."  There  are 
few  people  capable  of  conceiving  the  effect 
which  reading,  thus  directed,  would  have  on 
youoig  minds. 


358  TJIE  YOUNG  MECHANIC. 

The  "  American  Biography"  of  Mr.  Sparks, 
in  ten  volumes,  is  a  work  of  great  merit.  Jt 
foims  a  part  of  Harper's  School  Library,  in 
which  may  be  found  many  other  biographical 
works  of  our  own  countrymen  as  well  as  of 
distinguished  foreigner*. 


ACCOMPLISHMENTS  IN  GENERAL.          359 

CHAPTER  XIII. 
THE  MECHANIC'S  STUDIES  CONTINUED. 

ACCOMPLISHMENTS  IN  GENERAL. 

A  PROPER  degree  of  attention  should  always 
be  paid  to  what  are  called  the  accomplishments 
of  life,  but  they  should  never  supersede  for  a 
moment  more  useful  studies.  Every  occupa- 
tion should  be  estimated  according  to  its  future 
utility,  and  as  those  points  which  are  deemed 
essential  to  the  demeanour  of  a  gentleman 
should  not  be  neglected,  and  demand  but  a 
small  portion  of  time  to  acquire,  a  pupil  should 
be  early  and  properly  attended  by  the  best 
masters  in  the  several  departments  of  drawing, 
music,  horsemanship,  and  dancing.  These  ac- 
complishments, and  the  art  of  swimming,  give 
a  suppleness  to  the  limbs,  a  grace  of  action, 
and  an  elegance  of  address  and  fine  taste 
which  always  obtain  the  favourable  preposses- 
sion of  the  company  to  whom  a  person  may 
be  introduced ;  but  talents  and  virtues  complete 
the  conquest  of  affection,  and  convert  the  pass- 


THE  YOUNG  MECHANIC. 

ing  applause  of  the  human  race  into  a  solid  and 
durable  esteem. 

A  copious  selection.,  says  Mr.  Yorke,  from 
the  excellent  letters  of  Lord  Chesterfield  to  his 
son,  are  always  before  my  pupil,  which  inspire 
him  with  a  laudable  desire  of  uniting  to  the 
character  of  a  man  of  knowledge,  the  accom- 
plishments of  a  gentleman.  The  object  of  in- 
struction is  to  make  men  better,  not  to  embrute 
them.  Whatever,  therefore,  is  deemed  auxiliary 
to  such  a  disposition,  should  be  encouraged. 
No  evil  can  arise  from  an  easy  address,  or  from 
agreeable  manners.  Politeness  is  the  handmaid 
of  civilization ;  perhaps  it  may  be  shown  to  be 
the  attendant  on  virtue.  Whatever  means, 
therefore,  are  judged  expedient  to  furnish  the 
opportunity  of  exhibiting  this  amiable  quality, 
are  commendable,  and  ought  to  be  adopted.  I 
allude,  in  this  instance,  to  genuine  politeness, 
not  to  that  false  affectation  of  good  manners^ 
which  consists  in  foppery  and  a  servile  imitation 
of  the  servile  manners  of  the  great,  and  of  men 
of  honour,  as,  by  a  strange  perversion  of  lan- 
guage, they  are  improperly  called.  The  term 
great  man,  is  so  equivocal,  says  Dr.  Beattie, 
that  I  will  have  nothing  to  do  with  it.  The 
vilest  scoundrel  on  earth,  if  possessed  of  a 


ACCOMPLISHMENTS  IN  GENERAL.  QQ^ 

crown  or  a  title,  immediately  commences  great 
man,  when  he  has  with  impunity  perpetrated 
any  extraordinary  act  of  wickedness ;  murder- 
ed fifty  thousand  men,  robbed  all  the  houses  in 
half  a  dozen  provinces,  or  dexterously  plun- 
dered his  own  country  to  defray  the  expense 
of  a  ruinous  war,  formed  to  satiate  his  avarice. 
The  term  honour  is  also  of  dubious  import 
According  to  the  notions  of  the  present  times, 
a  man  may  sell  his  country,  murder  his  friend, 
pick  the  pocket  of  his  fellow  sharper,  and  em- 
ploy his  whole  life  in  seducing  others  to  vice 
and  perdition,  and  yet  be  accounted  a  man  of 
honour ;  provided  he  be  accustomed  to  speak 
certain  words,  wear  certain  clothes,  and  haunt 
certain  company.  To  the  pernicious  influence 
of  this  unnatural  law  of  honour  the  just  senti- 
ments of  Archdeacon  Paley  may  be  applied. 
"  It  is  a  law,"  says  he,  "  which,  being  consti- 
tuted by  men  occupied  in  the  pursuit  of  plea- 
sure, and  for  the  mutual  convenience  of  such 
men,  will  be  found,  as  might  be  expected  from 
the  character  and  design  of  the  law  makers,  to 
be,  in  most  instances,  favourable  to  the  licen- 
tious indulgence  of  the  natural  passions.  Thus, 
it  allows  of  fornication,  adultery,  drunkenness, 
prodigality,  duelling,  and  revenge  in  the  ^x- 


3(32  THE  YOUNG  MECHANIC. 

treme ;  and  lays  no  stress  upon  the  virtues  op- 
posite to  these." 

If  any  additional  supports  were  necessary  in 
behalf  of  the  argument  that  bodily  accom- 
plishments may  be  considered  as  a  component 
part  of  the  happiness  and  perfection  of  man, 
we  might  introduce  the  powerful  authorities  of 
Mr.  Locke  and  Dr.  Watts,  who  have  applauded 
this  mode  of  instruction,  when  limited  to  such 
views.  The  latter  was  a  man  of  singular  piety, 
modesty,  and  uprightness ;  the  former  was  as 
much  distinguished  for  the  elegance  of  his 
manners,  as  for  his  knowledge  of  the  world, 
and  his  deep  insight  into  the  powers  of  the 
human  mind. 

TASTE. 

Taste  is  that  power,  which  the  mind  pos- 
sesses, of  relishing  the  beauties  found  in  the 
works  of  nature  and  art. 

Say  what  is  Taste,  but  the  internal  powers, 
Active  and  strong,  and  feelingly  alive 
To  each  fine  impulse  1  a  discerning  sense, 
Of  decent  and  sublime,  with  quick  disgust 
From  th:  igs  deform'd. 

It  has  beeu  alleged  that  Taste  is  a  natural  taleni 
as  independent  of  art  as  strong  eyes,  or  a  deli 


TASTE.  363 

cate  sense  of  smelling ;  and,  without  all  doubt^ 
the  principal  ingredient  in  the  composition  of 
taste  is  a  natural  sensibility,  without  which  it 
cannot  exist ;  but  it  differs  from  the  senses  in 
this  particular,  that  they  are  finished  by  nature ; 
whereas  taste  cannot  be  brought  to  perfection 
without  proper  cultivation :  for  taste  pretends 
to  judge  not  only  of  nature,  but  also  of  art; 
and  that  judgment  is  founded  upon  observation 
and  comparison. 

Though  nature  should  have  done  her  part, 
by  implanting  the  seeds  of  taste,  great  pains  must 
be  taken,  and  great  skill  exerted,  in  raising 
them  to  a  proper  pitch  of  vegetation.  The 
judicious  tutor  must  gradually  and  tenderly 
unfold  the  mental  faculties  of  the  youth  com- 
mitted to  his  charge.  He  must  cherish  his 
delicate  perception ;  store  his  mind  with  proper 
ideas ;  point  out  the  different  channels  of  ob- 
servation ;  teach  him  to  compare  objects ;  to 
establish  the  limits  of  right  and  wrong,  of  truth 
and  falsehood ;  to  distinguish  beauty  from  tin- 
sel, and  grace  from  affectation ;  in  a  word,  to 
strengthen  and  improve  by  culture,  experience, 
and  instruction,  those  natural  powers  of  sensi- 
bility and  sagacity,  which  constitute  the  faculty 
31 


36  i  THE  YCUNG  MECHANIC. 

called  taste,  and  enable  the  possessor  to  enjoy 
the  delights  of  elegant  learning.* 

I  do  not  call  taste  a  species  of  judgment, 
although  it  be  actually  that  part  of  judgment, 
whose  objects  are  the  sublime,  beautiful  and 
affecting ;  because  this  kind  of  judgment  is  not 
the  result  of  reason  and  comparison,  like  a 
mathematical  inference,  but  is  perceived  instan- 
taneously, and  obtruded  on  the  mind,  like  sweet 
and  bitter  on  the  sense,  from  which  analogy  it 
has  borrowed  the  name  of  taste.f 

Taste  presides  with  supreme  authority  over 
all  the  elegant  arts.  There  are  none  so  low  in 
their  subserviency  to  the  uses  of  mankind,  as 
not  to  afford  subjects  for  its  decisions.  It  ex- 
tends its  influence  to  dress,  furniture,  and  equip- 
age ;  but  presides,  as  in  its  most  distinguished 
and  eminent  provinces,  over  poetry,  eloquence, 
painting,  architecture,  sculpture,  and  music ; 
because  among  them  genius  takes  its  unbound- 
ed range,  ant1  exerts  its  fullest  power.  Taste 
is  derived  from  the  concurrent  voices  of  men 
of  various  ages  and  nations,  possessed  of  en- 
larged and  cultivatedfcunderstandings,  who  have 
lurveyed  the  works  of  genius  with  close  atten- 

*  Goldsmith.  f  Usher's  C  li  o. 


TASTE. 


don,  and  have  recorded  in  animated  descriptions 
the  impressions  made  upon  their  minds.  This 
authority  has  stamped  its  approbation  upon 
works  which  have  obtained  the  general  ap- 
plause of  all  ages  and  countries,  and  must  still 
continue  to  produce  a  similar  effect,  so  long  as 
the  intellectual  powers  of  man  remain  the  same; 
so  long  as  his  imagination  and  sensibility  are 
capable  of  being  affected  by  all  which  is  beau 
tiful,  pathethic  and  niblime. 

The  advance  of  national  taste  is  similar  to 
the  progress  of  taste  from  childhood  to  man- 
hood. When  the  attention  of  an  unpolished 
people  is  first  directed  to  works  of  art,  they  are 
captivated  by  mere  novelty  ;  and  the  rudest 
paintings  and  most  unpolished  verses  obtain 
their  applause.  In  proportion  as  superior  efforts 
of  genius  are  made,  the  opinion  of  the  judi- 
cious part  of  the  public,  at  least,  becomes 
more  correct;  and  what  at  first  delighted  is 
finally  rejected  with  disapprobation.  As  soon 
as  comparisons  are  made  between  different  pro- 
ductions of  the  same  kind,  true  taste  is  brought 
into  action,  its  decisions  are  called  for,  and  the 
justness  of  its  discriminations  is  universally 
acknowledged.  The  polished  contemporaries 
of  Horace  blushed  at  the  praises  which  their 


366  THE  YOUNG  MECHANIC. 

ancestors  had  bestowed  on  the  rude  dialogues 
of  Plautus,  and  were  charmed  with  the  polite 
and  elegant  comedies  of  Terence. 

The  lower  orders  of  society  are  disqualified 
from  deciding  on  the  merits  of  the  fine  arts ; 
and  the  department  of  taste  is  consequently 
confined  to  persons  enlightened  by  education, 
and  conversant  with  the  world,  whose  views 
of  nature,  art,  and  mankind,  are  enlarged  by  an 
extensive  range  of  observation,  and  elevated  far 
above  gross  ignorance  and  vulgar  prejudice.* 

The  general  rudiments  of  taste  are  to  be  ac- 
quired first  by  reading  books,  which  treat  pro- 
fessedly on  the  subject.  Secondly,  by  select- 
ing and  explaining  beautiful  passages  in  Shaks- 
peare,  Johnson,  Sterne,  &c.  And  lastly,  by  exhi- 
biting and  explaining  prints  of  beautiful  objects, 
or  casts  of  the  best  antique  gems  and  meda- 
lions.  Authors  have  divided  the  objects  of 
taste  into  the  sublime,  the  beautiful,  and  the 
new;  but  another  sect  of  inquirers  into  this 
subject  have  lately  added  the  picturesque ; 
which  is  supposed  to  differ  from  the  beautiful 
by  its  want  of  smoothness,  and  from  the 
sublime,  from  its  want  of  size.f 

*  Mr.  H.  Kett. 

fSee  Essay  on  the  Picturesque,  by  U.  Price,  Esq. 


TASTE.  367 

Others  have  endeavoured  to  make  a  distinc- 
tion between  beauty  and  grace,  and  have  e» 
teemed  them  a  kind  of  rivals  for  the  possession 
of  the  human  heart.  By  grace  may  be  defined 
beauty  in  action ;  for  a  sleeping  beauty  cannot 
be  called  graceful,  in  whatever  attitude  she  may 
recline ;  the  muscles  must  be  in  action  to  pro- 
duce a  gracefrl  attitude,  and  the  limbs  to  pro- 
duce a  graceful  motion.* 

Taste,  says  Lord  Kaimes,  is  one  of  our  facu1 
ties  which  is  the  slowest  in  its  progress  toward- 
maturity ;  and  yet  may  receive  some  improve- 
ment during  the  course  of  domestic  education. 
Compare  with  your  pupils  two  poems  on  the 
same  subject,  or  two  passages.  Take  the  lead  in 
pointing  out  beauties  and  blemishes,  in  the  sim- 
plest manner.  Aft^r  so  me  time,  let  them  take  the 
lead  under  your  correction.  You  cannot  have  a 
better  book  for  that  exercise  than  the  Spectator. 
A  pleasing  vein  of  genteel  humour  runs  through 
every  one  of  Addison's  papers,  which  like  the 
sweet  flavour  of  a  hyacinth,  constantly  cheers, 
and  never  overpowers.  Steele's  papers,  on  the 
contrary,  are  little  better  than  trash ;  there  is 
scarcely  a  thought  or  sentiment  which  is  worthy 

*  Dr.  Darwin's  Plan  of  Education. 


368  THE  YOUNG  MECHANIC 

to  be  transferred  into  a  common-place  book. 
My  pupil  reads  a  few  papers  daily  without  a 
single  observation  on  my  part.  After  some 
time,  I  remark  to  him  the  difference  of  compo- 
sition, which,  in  the  course  of  reading,  becomes 
more  and  more  apparent.  The  last  step  is  to 
engage  him  in  distinguishing  the  two  authors. 
He  at  first  made  awkward  attempts ;  from  fre- 
quent trials,  he  began  to  distinguish.  Now  he 
will  almost  in  the  first  period  cry,  "  Foh !  this 
is  Steele,  let  us  have  no  more  of  him." 

If  we  wish  to  be  directed  to  authors,  who 
were  eminent  for  correctness  of  taste,  we  may 
select  in  painting  Fresnoy,  Vasari,  and  Rey- 
nolds ;  in  music,  Burney ;  in  eloquence,  Cicero 
and  Quintilian ;  and  in  poetry,  Horace,  Pope, 
Gray,  and  the  Wartons.  These  were  critics, 
who  had  the  singular  merit  of  teaching  that  art 
in  which  they  were  themselves  distinguished ; 
and  their  own  works  are  an  example  and  an 
illustration  of  their  rules.* 

It  is  no  wonder  that  wholly  uneducated  people 
want  elegance  and  taste.  It  is  not  from  them 
that  we  are  to  seek  the  natural  bias  of  the  soul 
The  necessaries  of  life,  when  they  are  to  be 

*  Mr.  H.  Kett's  Elements. 


DRAWING. 

procured  by  an  individual  for  a  wife  and  nume- 
rous young  children  are  procured  by  vast  la- 
bour and  hardship.  Labour  requires  strained, 
forced,  and  violent  motions.  This  race  of  men 
walk  not  for  pleasure,  but  to  perform  journeys 
of  necessity.  They  take  advantage  therefore 
of  bending  the  body  forward,  and  assisting  their 
motion  by  a  sling  with  their  arms.  Their  low 
station,  their  wants,  and  their  drudgeries,  give 
them  a  sordidness  and  ungenerosity  of  disposi- 
tion, together  with  a  coarseness  and  nakedness 
of  expression ;  whence  their  motions  and  ad- 
dress are  equally  rude  and  ungraceful.  This 
dishonoured  state  of  man  is  the  offspring  of  his 
wants,  and  of  the  miseries  which  yoke  him 
down  a  slave  to  the  globe  which  he  tills,  and 
depress  together  his  mind  and  his  body.* 

DRAWING. 

Drawing  is  not  only  an  accomplishment  the 
-nost  elegant,  agreeable,  and  ornamental,  but,  at 
the  same  time  that  it  is  the  foundation  of  paint- 
ing, is  of  the  utmost  utility  to  the  sculptor,,  the 
civil  and  naval  architect,  the  engraver,  the  en- 
gineer, the  mathematician,  and  navigator.  It 

•Clio. 


370  TfIE  ^*>UNG  MECHANIC. 

also  assists  the  gardener,  the  cabinet  maker,  thr 
weaver,  &,c.  In  short,  there  is  scarcely  a  branch 
of  civil  society  which  is  not  indebted  to  it,  from 
the  maker  of  the  iron  rails  before  our  house,  to 
the  tea  urn  on  our  table.  To  it  we  are  indebt- 
ed for  representations  of  those  elegant  remains 
of  antiquity  which  have  contributed  so  much 
to  the  advancement  of  our  knowledge  of  fine 
form.  Volumes  of  verbal  description  will  not 
convey  so  true  an  idea  of  an  object,  as  the 
slightest  outline.  Hence  the  source  of  much 
of  our  knowledge  in  antiquity,  of  which  Ian 
guage  could  convey  no  adequate  idea.  To  be 
able  on  the  spot  to  make  a  sketch  of  a  fine 
building,  beautiful  prospect,  or  any  curious  pro- 
duction of  nature  or  of  art,  is  not  only  a  very 
desirable  and  elegant  accomplishment,  but  in 
the  highest  degree  entertaining.  To  treasure 
up  whatever  may  occur  in  our  travels,  either 
for  future  use  or  to  illustrate  conversation,  to 
represent  the  deeds  of  former  ages,  to  preserve 
the  features  of  our  most  valued  friends,  has 
made  this  art  not  only  one  of  the  highest  em- 
bellishments of  our  nature,  but  the  delight  of 
$11  ages.  The  greatest  writers  have  united  to 
praise,  and  empires  to  encourage  it.  It  has 
been  in  the  highest  degree  morally  useful ;  and 


DRAWING.  37j 

where  it  has  flourished,  conferred  honour  on 
the  country.* 

It  is  impossible  to  judge  accurate! y  of  the 
dimensions  of  bodies,  unless  we  learn  also  to 
know  their  figures,  and  even  to  imitate  those 
figures  ;  for  this  imitation  is  founded  on  nothing 
else  but  the  rules  of  perspective,  and  we  can- 
not estimate  the  extension  of  bodies  by  their 
appearance,  unless  we  have  some  knowledge 
of  those  rules.  Children,  being  great  imitators, 
all  attempt  to  design ;  I  will  have  my  pupil, 
says  Rousseau,  cultivate  that  art ;  not  so  much 
for  the  art  itself,  as  for  the  sake  of  giving  him 
a  good  eye  and  a  flexible  hand.  I  will  take 
care  that  he  shall  rarely  imitate  imitations.  He 
should  have  before  his  eyes  the  original  itself, 
and  not  the  paper  representing  it.  Thus  he 
should  design  a  house  from  a  house,  a  tree  from 
a  tree,  a  man  from  a  man,  that  he  may  be  ac- 
customed to  observe  minutely  and  accurately 
the  appearance  of  bodies,  and  not  take  false  and 
artificial  imitations  for  those  which  are  true  and 
genuine.  I  would  even  discourage  him  from 
endeavouring  to  trace  any  tiling  from  memory, 
till  by  frequent  and  repeated  observations,  its 

*  Mr.  E.  Dayes  in  Mr.  Tilloch's  Philosop.  Mag.  vol 
Xiv.  219. 


372  THE  YOUNG  MECHANIC. 

figure  should  be  strongly  imprinted  on  his 
imagination ;  lest  he  should  otherwise,  by  sub- 
stituting some  fantastic  image  instead  of  the 
real  one,  lose  the  knowledge  of  proportion,  and 
a  taste  for  the  genuine  beauties  of  nature. 

If  my  pupil  wishes  to  become  a  painter,  he 
does  not  commence  his  career  by  a  dry  study 
of  lines  ;  he  does  not  "  imitate  imitations  ;"  he 
paints  from  nature.  At  the  same  time,  that  he 
may  not  lose  the  advantages  derived  from  the 
labours  of  past  ages,  he  submits  his  productions 
to  a  master  of  the  art,  who  may  correct  his 
errors  and  accelerate  his  improvement.  So  in 
electricity,  chemistry,  &c.,  he  begins  by  experi- 
ment, under  the  eye  of  a  master,  and  thence 
either  deduces  his  own  general  rules,  or  con- 
firms those  of  others.* 

MUSIC. 

Music  may  be  considered  one  of  the  most 
usefal  means  which  we  possess  of  improving 
and  cultivating  the  mind  of  man,  and  by  far  the 
most  powerful  in  softening  the  heart,  and  ren- 
dering it  susceptible  of  every  fine  and  more 
Baited  sentiment.  Nor  can  music  be  called 

*  *  Northmore. 


MUSIC.  373 

merely  an  art  calculated  to  please  and  delight 
he  senses  alone,  for  certainly  its  execution 
employs  the  mind  much  more  than  the  body. 
To  instance  the  many  surprising  effects  pro- 
duced by  music  over  the  minds  of  men,  even 
the  most  rude  and  barbarous,  would  be  super- 
fluous and  impertinent.  The  delight  which 
music  imparts  to  the  mind,  can  be  enjoyed  in 
every  period  of  life,  from  the  earliest  infancy 
to  the  total  decay  of  all  vital  powers.  No  art 
affording  so  much  felicity  and  happiness  can 
be  so  easily  cultivated  and  attained.  The  in- 
fluence of  this  part  of  education  over  the  mind 
of  the  female  sex,  must  be,  and  certainly  is, 
highly  beneficial.  Their  hearts  are  hence  in  a 
particular  manner  cultivated  and  refined,  and 
those  sensations  are  exercised  and  strengthened 
in  their  bosoms,  which  render  them  peculiarly 
lovely  and  amiable.  Many  females,  however, 
are  entirely  deprived  of  the  advantages  result- 
ing from  this  part  of  education. 

It  is  sincerely  to  be  lamented  and  regretted, 
that  the  truly  respectable  sect  of  Quakers  should 
forbid  the  cultivation  and  practice  of  music  in 
their  societies;  and  it  is  wonderful  that  the 
effects  which  already  have  resulted  from  this 
prohibition,  have  not  yet  convinced  them  of  the 


374  TIIE  YOUNG  MECHANIC. 

impropriety  and  pernicious  tendency  of  their 
unreasonable  prejudice  against  music.  Such 
indeed  are  the  effects  produced  by  the  total 
neglect  of  this  divine  art  among  the  society  of 
Friends,  that  the  tones  of  their  voice  in  reading 
and  public  speaking  are  so  harsh  and  discordant 
as  scarcely  to  be  endured  by  a  person  of  a  nice 
and  delicate  musical  ear.  The  worship  of  the 
catholic  church,  and  that  of  the  quakers,  are  in 
this  respect  as  opposite  as  possible.  The 
catholics  chant  their  worship,  and  its  influence 
is  thereby  augmented. 

The  bravery  and  independence  of  the  Swiss 
*e  universally  known,  and  in  no  people,  per- 
haps, is  the  influence  of  pathetic  music  so  pow- 
erfully exerted.  The  inhabitants  of  many  other 
mountainous  countries  afford  striking  examples 
of  the  same  kind.  No  people  are  more  pos- 
sessed of  true  independence  of  mind  than  the 
inhabitants  of  the  Highlands  of  Scotland,  and 
in  no  country  are  the  softer  sensibilities  of  the 
heart  more  cultivated  and  indulged.  I  have 
never  yet  known  an  instance  of  a  person  capa- 
ble of  enjoying  all  the  ecstacy  of  musical  de- 
light whose  heart  was  not  warm,  tender  and 
benevolent.* 

*  Dr.  Cowan. 


DANCING.  375 

DANCING. 

The  design  of  this  accomplishment  is  to  ob- 
tain a  graceful  carriage,  and  a  pleasing  address 
on  all  occasions.  It  has  been  said,  that  "  no 
person  can  either  sit,  stand,  or  walk  well,  un- 
less he  dances  well."  This  is  certainly  carry- 
ing tJie  matter  too  far.  There  are  some  who 
never  so  much  as  learned  a  step,  who  both  sit, 
stand.,  and  walk  with  more  grace  than  some 
professed  dancing  masters.  This  art,  however, 
frequently  teaches  young  people  to  walk  with 
firmness  and  ease,  to  enter  a  room  gracefully, 
to  incline  the  head  or  body,  even  when  sitting 
and  conversing,  without  any  distortion ;  and 
removes  that  awkward  stiffness,  which  in 
country  people  who  have  not  had  the  advan- 
tages of  a  good  education,  is  so  apparent.  To 
obtain  great  perfection  in  this  art,  though  it  be 
necessary  for  professional  performers,  would  be 
a  shameful  waste  of  time,  which  might  be  infi- 
nitely better  employed  in  mental  attainments. 

POLITENESS. 

There  is  a  fascinating  manner  in  the  address 
of  some  people,  which  almostly  instantly  con- 
ciliates the  good- will,  and  even  the  confidence 
32 


376  THE  YOUNG  MECHANIC. 

of  their  acquaintance.  Machiavel  in  his  his- 
tory of  Castruccio  Castricani  observes,  that  his 
hero  could  assume  such  openness  of  counte- 
nance, that  though  he  was  known  to  be  a  man 
practised  in  every  art  of  fraud  and  treachery, 
yet  in  a  few  minutes  he  gained  the  confidence 
of  all  whom  he  conversed  with;  they  went 
away  satisfied  of  his  good  will  towards  them, 
and  were  betrayed  to  their  ruin.  This  enviable 
address,  which  may  be  used  for  good  purposes 
as  well  as  bad  ones,  is  difficult  to  analyse ;  it 
may  possibly  consist  simply  in  a  countenance 
animated  with  pleasure  at  meeting  and  con- 
versing with  our  acquaintance ;  and  which  dif- 
fuses cheerfulness  by  pleasurable  contagion 
into  the  bosoms  of  others ;  and  thus  interests 
them  in  our  behalf.  It  is  net  the  smile  of  flat- 
tery, nor  the  smile  of  self-approbation,  nor  the 
smile  of  habit,  nor  of  levity ;  but  it  is  simply 
an  expression  of  pleasure,  which  seems  to  arise 
at  the  sight  of  our  acquaintance;  and  which 
persuades  them,  that  they  possess  our  love,  for 
which  they  barter  their  own  in  return.  How- 
ever this  conciliating  manner  may  have  beer 
used,  as  above  related,  for  bad  purposes,  it  pro 
bably  proceeded  originally  from  friendliness 
%nd  openness  of  heart,  with  cheerful  benevo 


POLITENESS.  377 

lence ;  and  that  in  those,  who  have  in  process 
of  time  become  bad  characters,  the  appearance 
of  those  virtues  has  remained,  after  the  reality 
of  them  lias  vanished.  What  then  is  the  method 
by  which  this  enchantment  of  countenance  can 
be  taught  ?  Certainly  by  instilling  cheerfulness 
and  benevolence  into  the  minds  of  young  peo- 
ple early  in  life,  and  at  the  same  time  an  anima- 
tion of  countenance  in  expressing  them ;  and 
though  this  pleasurable  animation  be  at  nrst 
only  copied,  it  will  in  time  have  the  appearance 
of  being  natural ;  and  will  contribute  to  pro- 
duce, by  association,  the  very  cheerfulness  and 
benevolence,  which  it  at  first  only  imitated. 
This  is  an  observation  to  which  those  who  have 
the  care  of  young  children  should  closely  attend. 
Next  to  the  winning  manners  above  described, 
the  art  of  pleasing  in  conversation  seems  to 
consist  in  two  things ;  one  of  them  to  hear 
well,  and  the  other  to  speak  well.  The  per- 
petual appearance  of  attention,  and  the  varying 
expression  of  the  countenance  of  the  hearer  to 
the  sentiments  or  passion  of  the  speaker,  is  a 
principal  charm  in  conversation;  to  be  well 
heard  and  accurately  understood  encourages 
our  companions  to  proceed  with  pleasure,  what- 
ever may  be  the  topics  of  their  discourse. 


378  THE  ™UNG  MECHANIC. 

To  speak  agreeably,  in  respect  to  manner, 
consists  in  a  voice  clear,  yet  not  loud ;  soft, 
yet  not  plaintive ;  with  distinct  articulation,  and 
with  graceful  attitudes  rather  than  with  graceful 
actions  ;  as  -almost  every  kind  of  gesticulation 
is  disagreeable.  In  respect  to  the  matter,  it 
should  be  such  as  coincides  with  the  tastes  or 
pursuits  of  those  to  whom  the  conversation  is 
addressed.  Hence  it  will  appear  that  to  hear 
well,  and  to  speak  well,  requires  an  extensive 
knowledge  of  things,  as  well  as  of  the  tastes 
and  pursuits  of  mankind ;  and  must  therefore 
ultimately  be  the  effect  of  a  good  education  in 
general,  rather  than  a  particular  article  of  it. 
There  are,  however,  faults  to  be  avoided,  and 
cautions  to  be  observed,  which  should  be  point- 
ed out  to  young  people.  Of  these  I  shall,  men- 
tion,— 1.  That  whenever  the  thirst  of  shining 
in  conversation  seizes  on  the  heart,  the  vanity 
of  the  speaker  becomes  apparent ;  and  we  are 
disgusted  with  the  manner,  whatever  may  be 
the  matter  of  the  discourse.  2.  That  it  is 
always  childish,  and  generally  ridiculous,  when 
young  people  boast  of  their  follies,  or  when 
they  accuse  themselves  of  virtues.  3.  They 
should  be  apprised,  that  there  is  danger  in 
speaking  ill  even  of  a  bad  person ;  both  be- 


POLITENESS.  379 

cause  they  may  have  been  misinformed,  and 
because  they  should  judge  their  neighbours 
with  charity.  A  friend  of  mine  was  once  asked 
how  he  could  distinguish  whether  the  lady, 
whom  he  meant  to  address,  was  good  temper- 
ed, and  gave  this  answer  :  "  When  any  dubious 
accusation  is  brought  in  conversation  against 
an  absent  person  ,  if  she  always  inclines  to 
believe  the  worst  side  of  the  question,  she  is 
ill  tempered."  There  are  some  nice  distinc- 
tions on  this  subject  of  good  nature  in  Lady 
Pennington's  Advice  to  her  Daughters,  whicb 
are  worth  the  attention  of  young  ladies.  4 
Strong  asseverations,  or  a  kind  of  petty  oaths, 
such  as  « upon  my  honour ;"  appealing  to 
others  for  the  truth  of  an  affirmation ;  an 
always  wrong,  because  such  strong  expression 
derogate  somewhat  from  the  character  of  the 
speaker,  as  they  intimate  that  a  simple  assertion 
may  not  be  believed.  5.  Loud  laughter,  or 
tittering  in  short  shrieks,  as  practised  by  some 
ladies  at  cards,  are  reprehensible.  Dignity  of 
character  always  suffers  by  being  violently 
agitated  at  trivial  circumstances.  6.  A  uniform 
adherence  to  sincerity  in  conversation  is  of  the 
first  importance.  No  artificial  polish  ol  man- 
ners can  compensate  for  the  apparent  want  of 
32* 


THE  YOUNG  MECHANIC 

this  virtue,  nor  any  acquirements  of  knowledge 
for  the  reality  of  such  a  want.  Opinions 
should  be  given  with  exact  truth,  if  given  at 
all ;  hut  when  the  characters  of  others  are  con- 
cerned, they  should  be  delivered  with  diffidence 
and  modesty.  Lastly,  a  marked  disapprobation 
should  always  be  shown  to  indecency,  immo- 
rality, or  irreligion.  In  the  softer  sex,  so  great  is 
their  power  in  meliorating  the  characters  of  men, 
that  if  profligacy,  infidelity,  and  debauchery, 
were  universally  despised,  the  morals  of  the 
age  would  be  entirely  reformed.  To  these 
might  be  added  many  other  observations  from 
various  writers,  concerning  a  due  respect  in  con- 
versation to  superiors,  good  temper  to  equals, 
and  condescension  to  inferiors ;  but  as  young 
people  are  not  expected  to  speak  with  the  wis- 
dom, or  precision  of  philosophers ;  and  as  the 
careless  cheerfulness  of  their  conversation,  with 
simplicity  of  manner,  and  with  grace,  ease,  and 
vivacity  natural  to  youth,  supplies  it  with  its 
principal  charms,  these  should  be  particularly 
encouraged,  as  there  are  few  artificial  accom- 
plishments, which  could  compensate  for  the 
Loss  of  them.* 

»  Dr.  Darwin. 


MORALS.  3QJ 

CHAPTER  XIV. 
THE  MORALS  OF  THE  MECHANIC. 

THE  only  lesson  of  morality  proper  for 
children,  and  the  most  important  to  persons  of 
all  ages,  is  never  to  do  an  injury  to  any  one. 
Even  the  positive  precept  of  doing  good,  if  not 
made  subordinate  to  this,  is  dangerous,  false, 
and  contradictory.  Who  is  there  who  does  no 
good  ?  All  the  world,  even  the  vicious  man, 
does  good  to  one  or  other  party  :  he  will  make 
one  person  happy  at  the  expense  of  making  a 
hundred  miserable  ;  hence  arise  our  calamities. 
The  most  sublime  virtues  are  negative ;  they 
are  also  the  most  difficult  to  put  in  practice, 
because  they  are  attended  with  no  ostentation, 
and  are  even  above  that  pleasure  so  flattering 
to  the  heart  of  man,  that  of  sending  away  others 
satisfied  with  our  benevolence.  Oh  how  much 
good  must  that  man  necessarily  do  his  fellow 
creatures,  if  such  a  man  there  be,  who  never 
did  any  of  them  harm!  The  injunction  of 
doing  no  one  harm,  infers  that  of  doing  the 
least  possible  harm  to  the  community  in  gene- 


382  TIIE  YOUNG  MECHANIC. 

ral ;  for  in  a  state  of  society  the  good  of  one 
man  necessarily  becomes  the  evil  of  another.* 

I  think  it  might  be  proved,  that  the  best  pre- 
cepts of  morality,  inculcated  even  under  the 
sanction  of  religious  awe,  are  not  of  half  the 
efficacy  in  the  prevention  of  vice,  as  a  taste  for 
reading  and  science.  Experience  informs  us 
how  soon  the  principles  of  morality  inculcated 
in  childhood  are  forgotten,  or  accommodated  to 
the  prevailing  customs  of  the  world  :  but  if  a 
taste  for  science  be  acquired,  the  affections  are 
then  fixed  upon  a  rational  object;  there  is  no 
temptation  to  allure  them  from  the  path  of  vir- 
tue ;  at  least  the  most  powerful  of  all  incite- 
ments to  criminal  amusements  is  removed,  the 
tediousness  of  life  during  the  intervals  of  lei- 
sure.! 

Plato  has  observed  with  great  propriety,  that 
the  end  of  the  education  and  instruction  of 
youth  as  well  as  the  end  of  government,  is  to 
make  men  better;  and  that  whoever  departs 
from  this  rule,  however  meritorious  lie  may 
otherwise  appear  to  be  in  reality,  deserves 
neither  the  esteem  nor  the  approbation  of  the 
public.  The  greatest  erudition  is  of  no  value, 

*  Rousseau,  b.  2.  -J-  Gregory's  Essays. 


MORALS.  gg^ 

if  unattended  with  probity.  It  is  worse,  it  is 
dangerous  to  the  welfare  and  tranquillity  of  so- 
ciety  Quintilian,  in  his  admirable  treatise,  has 
laid  it  down  as  a  rule  in  forming  a  perfect  orator, 
that  none  but  an  upright  man  can  merit  that 
name,  and  therefore  he  asserts  as  a  necessary 
qualification,  that  he  should  not  only  speak 
well,  but  also  possess  all  the  moral  virtues.  Mr. 
Justice  Blackstone  has  wisely  adopted  a  similar 
opinion  in  his  introductory  lecture  on  the  study 
of  the  law,  in  which,  after  having  enumerated 
all  the  qualities  of  the  head,  he  adds  to  them 
those  of  the  heart,  as  indispensably  necessary 
to  form  a  truly  valuable  English  lawyer,  a  Hyde, 
a  Hale,  or  a  Talbot.  And  Dr.  Blair  has,  with 
great  elegance  and  propriety,  suggested  the  same 
idea  as  a  necessary  ingredient  in  the  character 
of  a  sublime  writer.  But  this  just  sentiment  is 
not  to  be  restricted  to  any  particular  profession 
or  order  of  men.  The  knowledge  and  prac- 
tice of  morality  is  the  voice  of  nature,  which 
is  unbounded  and  universal :  and  however  ex- 
pedient it  may  be  in  those  whose  stations  in 
life,  render  them  objects  of  imitation  or  esteem, 
to  perform  with  the  most  rigid  punctuality 
every  moral  duty,  it  must  not  be  forgotten,  that 
the  conviction  of  the  utility  of  the  practice, 


3S4  THE  YOUNG  MECHANIC. 

should  make  it  the  common  sense  and  common 
respect  of  all  mankind. 

The  general  rules  of  morality  are  formed  by 
a  constant  observation  of  the  fitness  and  pro- 
priety of  actions  in  other  men.  What  is  fit  to 
be  done,  and  what  excites  universal  applause, 
not  only  calls  forth  our  own  approbation,  but 
warms  us  into  a  spirit  of  imitation.  What 
ought  to  be  avoided,  we  discover  in  the  general 
sentiment  of  detestation  which  attends  the  per- 
petration of  crime.  The  propriety  of  the  former 
and  the  deformity  of  the  latter  quickly  excite 
our  emulation  or  abhorrence.  We  soon  esta- 
blish a  general  rule  for  the  regulation  of  our 
conduct,  which  receives  a  full  confirmation  from 
the  opinion  of  the  rest  of  mankind.  It  is  thus 
that  the  general  rules  of  morality  are  formed. 
They  are  ultimately  founded  upon  experience 
of  what,  in  particular  instances,  our  moral 
faculties,  our  natural  sense  of  merit  and  pro- 
priety, approve  or  disapprove  of.  We  do  not 
originally  approve  or  condemn  particular  ac- 
tions ;  because,  upon  examination,  they  appear 
to  be  agreeable  or  inconsistent  with  a  certain 
general  rule.  The  general  rule,  on  the  contrary, 
is  formed  by  finding  from  experience  that  all 
actions  of  a  certain  kind,  or  circumstanced  in 


MORALS. 

certain  manner,  are  approved  or  disapproved 
of.  An  amiable  action,  a  respectable  action, 
a  horrid  action,  are  all  of  them  actions  which 
naturally  excite  for  the  person  who  performs 
them,  the  love,  the  respect,  or  the  horror  of  the 
spectator.  The  general  rules  which  determine 
what  actions  are,  and  what  are  not,  the  objects 
of  each  of  those  sentiments,  can  be  formed  no 
other  way  than  by  observing  what  actions  ac- 
tually and  in  fact  excite  them.  The  regard  to 
those  general  rules  of  conduct,  is  what  is  pro- 
perly called  a  sense  of  duty,  a  principle  of  the 
greatest  consequence  in  human  life,  and  the 
only  principle  by  which  the  bulk  of  mankind 
are  capable  of  directing  their  actions.  Without 
this  sacred  regard  to  general  rules,  there  is  no 
man  whose  conduct  can  be  so  much  depended 
upon.  It  is  this  which  constitutes  the  most 
essential  difference  between  a  man  of  principle 
and  honour,  and  a  worthless  fellow.  The  one 
adheres  on  all  occasions,  steadily  and  resolutely 
to  his  maxims,  and  preserves  through  the  whole 
of  his  life,  one  even  tenor  of  conduct.  The 
other  acts  variously  and  accidentally,  as  humour 
inclination,  or  interest  chances  to  be  uppermost. 
On  the  most  scrupulous  observance  of  these 
rules  of  conduct,  depends  the  very  existence 


388  THE  YOUNG  MECHANIC 

and  happiness  of  human  society,  which  would 
crumble  into  nothing  if  mankind  were  not 
generally  impressed  with  a  reverence  for  them. 
«  Among  the  many  fortuitous  events  which 
spring  up  daily  in  the  world,  opportunities  of 
inculcating  a  moral  lesson  frequently  present 
themselves ;  and  when  the  mind  has  habituated 
itself  to  inquiry  and  discrimination,  it  will 
insensibly  acquire  a  considerable  degree  of 
acumen,  which  may  hereafter  be  employed 
with  great  emolument.  For  as  it  developes  its 
powers  of  reasoning,  it  will  direct  this  habit  to 
other  purposes  of  life,  and  virtue  will  have  so 
strengthened  its  seat  in  the  understanding,  that 
its  principles  will  be  both  relished  and  admired 
when  at  a  future  period  they  are  examined  ab- 
stractedly. It  is  for  this  reason,  we  cannot  too 
often,  after  having  laid  down  a  moral  principle, 
proceed  to  explain  it  by  a  practical  illustration. 
A  very  little  industry  will  qualify  any  one  for 
this  undertaking.  The  same  volubility  of 
speech  which  is  often  admirably  exerted  to 
propagate  the  villanous  reports  of  scandal,  and 
to  tear  piecemeal  the  domestic  happiness  of 
others,  may  be  diverted,  by  this  means,  to  an 
honourable  and  useful  end. 


RELIGION.  ggi* 

RELIGION. 

Disbelief  or  distrust  of  the  truth  of  Chris- 
tianity arises  in  different  men  from  different 
causes.  Some  who  have  been  much  accustomed 
to  foreign  travel,  and  have  beheld  opposite  re- 
ligions firmly  established  in  different  countries, 
on  the  contrary  sides  of  the  same  mountain,  or 
the  neighbouring  banks  of  the  same  river;  and 
others  who  have  learnt  from  the  records  of  his- 
tory that  various  systems  of  faith  have  suc- 
cessively prevailed  in  the  same  country ;  that 
they  have  been  changed  again  and  again  within 
very  short  periods ;  and  that  each  in  its  day 
has  been  implicitly  received,  and  has  produced, 
or,  if  an  occasion  offered,  could  have  produced 
its  martyrs ;  such  persons  are  sometimes  prone 
to  form  what  they  term  the  liberal  conclusion, 
that  all  religions  are  alike.  They  assert  that  the 
Supreme  Being  has  enabled  mankind  to  disco- 
ver, by  the  reasoning  faculty  with  which  he 
has  endowed  them,  those  plain  precepts  of  mo- 
rality, the  observance  of  which  is  the  only 
service  required  by  him  ;  and  that  the  object 
of  all  religions,  however  they  may  be  encum- 
bered with  fanatical  rites  and  doctrines,  which, 
in  everv  country,  the  wise  will  inwardly  regard 
33 


388  THE  YOUNG  MECHANIC. 

with  contempt  is  to  inculcate  the  obligation  of 
those  precepts.  Or  they  boldly  pronounce  that 
religion  of  every  kind  is  superstition :  in  other 
words,  that  though  certain  modes  of  conduct 
ought  to  be  followed,  and  others  to  be  ex- 
ploded, from  principles  of  honour,  and  for  the 
good  of  society ;  to  deem  men  bound  to  act  in 
any  case  with  a  reference  to  a  supposed  will  of 
the  Deity,  if  a  Deity  exists,  is  of  all  absurdities 
the  grossest.  Others  again,  who  have  addicted 
themselves  to  philosophical  investigations,  have 
become  decided  unbelievers.  Not  that  philoso- 
phy is  the  enemy  of  religion.  The  former  is 
the  natural  ally  of  the  latter.  An  inquiry  into 
the  laws  which  God  has  prescribed  to  the  hu- 
man mind,  to  organized  bodies,  and  to  inanimate 
matter,  leads  at  every  step  to  a  new  display  of 
his  power,  wisdom  and  goodness.  But  men 
who  pursue  it  without  any  aim  or  desire  to 
apply  it  to  its  most  important  use,  that  of 
heightening  their  reverence  for  the  great  Creator 
by  a  nearer  acquaintance  with  his  glorious  at- 
tributes, easily  become  absorbed  in  the  contem- 
plation of  second  causes ;  and,  though  they  may 
admit  the  existence,  learn  to  deny  the  superin- 
tending care  of  the  First  Cause,  and  his  interfe- 
-ence  with  the  course  of  the  material  or  the 


RELIGION. 

moral  world.  Others  seek  for  refuge  in  unbelief, 
on  the  same  principle  on  which  many  of  the  Jews 
did  in  the  days  of  Christ ;  who  "  loved  dark- 
ness rather  than  light,  because  their  deeds  were 
evil,  and  would  not  come  to  the  light  lest  their 
deeds  should  be  reproved."  Resolved  to  per- 
sist in  the  vicious  practices  which  Christianity 
proscribes,  they  take  pains  to  convince  them- 
selves that  the  gospel  is  the  production  of  fraud 
and  delusion ;  they  catch  eagerly  at  every  ob- 
jection against  it  of  every  kind,  and  turn  from 
whatever  seems  to  make  in  its  favour ;  in  the 
language  of  scripture,  they  wink  purposely 
with  their  eyes  lest  they  should  see,  and  shut 
their  ears  lest  they  should  hear,  and  harden, 
their  hearts  lest  they  should  believe.  Others 
by  degrees  becoming  altogether  immersed  in 
political,  commercial,  or  professional  business, 
or  in  a  continued  succession  of  dissipated 
amusements,  proceed  from  the  omission  of  the 
practices  of  religious  duties  to  the  disuse  and 
disregard  of  religious  considerations,  and  ulti- 
mately to  the  disbelief  of  revealed  religion,  if 
not  of  all  religion.  And  lastly,  disdain  of  think- 
ing with  the  vulgar,  disgust  at  casual  instances 
uf  superstition,  and  difficulties  as  to  particular 


390  THE  YOUNG  MECHANIC. 

doctrines,  occasionally  contribute  to  lead  me* 
to  unbelief. 

Besides  the  confirmed  unbelievers  of  each  of 
these  descriptions,  there  are  many  persons  who 
from  various  causes,  advance  only  part  of  the 
way  on  the  road  to  infidelity,  and  stop  short  at 
different  stages  of  doubt  and  distrust. 

Concerning  unbelievers  and  doubters  of  every 
class,  one  observation  may  almost  universally 
be  made  with  truth ;  that  they  are  little  ac- 
quainted with  the  nature  of  the  Christian  reli- 
gion, and  still  less  with  the  evidence  by  which 
its  truth  is  supported. 

Now  those  who  question  or  deny  the  truth 
of  Christianity  will  yet  readily  admit,  that  if  the 
Supreme  Being  has  actually  made  a  revealed 
communication  of  his  will,  and  has  unequivocal- 
ly addressed  it  to  all  mankind  ;  and  if  there  are 
facts  connected  with  that  revelation  which  are 
acknowledged  even  by  its  enemies,  and  which 
justly  afford,  independently  of  other  evidence, 
a  strong  presumption  of  its  reality ;  those  per- 
sons must  be  highly  guilty,  who,  having  suffi- 
cient abilities  and  opportunities  for  inquiry,  re- 
fuse or  neglect  to  examine  into  the  validity  of  its 
pretensions;  and  to  examine  with  fairness, and 
with  the  attention  which  the  subject  demands 


RELIGION.  391 

Is  it  then  a  thing  highly  improbable  in  itself 
that  the  Creator  of  the  world  should  have  given 
a  revelation  to  mankind,  and  at  the  period  when 
Christianity  first  appeal  ed  ?  If  the  present  stage 
of  existence,  is  but  a  very  small  part  of  the 
whole  duration  of  a  human  being ;  if  this  stage 
is  designed  for  the  purpose  of  trial  and  proba- 
tion, and  is  thus  to  fix  the  state  of  each  indivi- 
dual for  ever ;  if  men  were  in  fact  ignorant  of 
the  certainty  of  these  momentous  truths,  and 
unable  to  ascertain  it  by  unassisted  reason  ;  if, 
for  want  of  a  knowledge  of  that  certainty,  they 
were  become  a  prey  to  crimes  and  delusions, 
indulging  themselves  in  every  species  of  wick- 
edness, and  worshipping  stocks  and  stones,  and 
personified  vices,  with  absurd  and  abominable 
rites ;  can  it  be  improbable  that  He  who  had 
manifested  his  goodness  in  creating  them,  should 
add  another  proof  of  the  same  disposition  by 
imparting  to  them  the  further  light  necessary 
to  correct  their  wanderings,  and  to  guide  them 
steadily  in  the  way  to  happiness  ? 

They  who  are  led  by  these  or  other  consi- 
derations to  regard  a  revelation  as  a  thing  not 
improbable  in  itself,  ought  from  that  circum- 
stance to  feel,  and  naturally  will  feel,  a  greater 
readiness  to  inquire  into  the  evidence  of  any 
33^ 


39-2  THE  YOUNG  MECHANIC. 

professed  revelation  which  bears  outward  marks 
of  reality.  They  who  deem  the  existence  of  a 
revelation  highly  improbable  cannot  affirm  that 
it  is  impossible ;  and  ought  consequently  in  a 
similar  case  to  institute  a  similar  inquiry.  For 
an  antecedent  persuasion  of  the  improbability 
of  the  Deity's  acting  in  any  particular  manner 
is  no  more  a  reason  for  refusing  to  examine 
whether  he  has  not  acted  thus,  if  existing  facts 
afford  strong  presumptive  evidence  that  he  has, 
than  it  would  be  for  refusing  to  believe  that  he 
has,  if  conclusive  evidence  were  produced. 

The  question  then  which  remains  to  be  an- 
swered is  this.  Are  there  any  leading  circum- 
stances attending  Christianity,  circumstances 
genera Uy  admitted,  and  resting  on  independent 
proofs,  which  seem  scarcely  capable  of  being 
accounted  for  on  any  supposition  but  on  that 
of  truth  ;  and  consequently  furnish  so  strong  a 
presumption  of  its  being  a  divine  revelation  as 
to  render  those  who  doubt,  or  deny  it,  not 
merely  imprudent  but  criminal,  if  they  do  not 
seriously  inquire  into  its  evidence  ? 

The  following  statement,  I  apprehend,  will 
justify  the  answering  of  that  questior.  decidedly 
in  the  affirmative. 

The  Christian  religion,  whether  true  or  false^ 


RELIGION.  393 

had  its  origin  in  a  country  and  nation  held  in 
proverbial  contempt  in  almost  every  part  of  the 
known  world.  The  author  of  the  religion  was 
not  only  a  Jew,  but  of  the  lowest  rank  among 
the  Jews.  He  is  universally  allowed  to  have 
been  uninstruc-ted  in  literature  and  philosophy. 
He  employed,  in  propagating  his  doctrine,  as- 
sistants who  were  also  Jews,  and  of  a  station 
as  obscure,  and  of  minds  as  little  cultivated  by 
learning,  as  his  own.  The  religion  which  they 
preached  was  of  such  a  nature  as  to  be  gene- 
rally and  unavoidably  most  obnoxious.  It  was 
avowedly  intended  to  supersede  and  annihilate 
every  other  religion.  It  attacked  not  only  the 
doctrines  and  ordinances  of  the  Jews,  which 
they  regarded  as  having  been  appointed  by  God 
himself;  but  those  inveterate  prepossessions 
which  were  rooted  no  less  firmly  in  their 
hearts ;  pronouncing  the  abolition  of  the  pecu- 
liar privileges  of  the  Jewish  race,  and  the  free 
admission  of  the  abhorred  Samaritans  and  Gen- 
tiles to  all  the  benefits  of  the  new  dispensation. 
It  not  only  exasperated  the  Romans  by  brand- 
ing as  impious  and  detestable  those  rites  and 
institutions  which  they  had  received  with  im- 
plicit reverence  from  their  remote  ancestors; 
and  deriding  as  vain  fictions  every  object  of 


394  THE  YOUNG  MECHANIC. 

their  adoration,  even  all  the  tutelary  deities  oi 
their  empire  ;  but  it  also  touched  their  jealousy 
in  the  tenderest  point,  by  suggesting  a  prospect 
of  the  revolt  of  Judea,  and  holding  forth  to 
their  imaginations  a  competitor  of  Ceesar,  and 
the  portentous  appearance  6f  the  long  expected 
sovereign,  whom  fate  had  destined  to  arise  in 
the  east.  The  founder  of  Christianity  had 
neither  the  favourable  circumstances  to  turn  to 
his  advantage,  of  which  other  teachers  of  new 
religions  have  availed  themselves ;  nor  did  he 
resort  to  those  methods  of  proceeding  to  which 
they  owed  their  success.  He  did  not,  like  Ma- 
homet, pay  court  to  a  particular  set  of  men,  or 
a  particular  sect ;  nor,  like  him,  artfully  conci- 
liate persons  of  all  the  different  religious  per- 
suasions in  the  country,  by  adopting  and  incor- 
porating into  his  own  system  some  of  the  prin- 
cipal of  their  respective  tenets ;  nor,  like  him, 
permit  licentious  indulgences  and  promise  licen 
tious  rewards  to  his  followers ;  nor,  like  him. 
direct  the  propagation  of  his  doctrine  by  the 
sword.  He  did  not  confine  his  instructions  to 
solitudes  and  obscure  hamlets ;  but  delivered 
them  in  the  most  public  manner,  in  populous 
cities,  in  the  most  frequented  parts  of  Jerusalem 
itself.  He  did  not  rest  his  pretensions  on  any 


RELIGION.  39/5 

species  of  evidence  of  a  secret  nature,  or  in 
any  respect  not  generally  cognizable  by  his  co- 
temporaries  ;  but  appealed  to  professed  miracles 
performed  in  the  sight  of  multitudes,  and  of 
such  a  kind  that  every  man  could  judge  as  to 
their  reafcty.  He  was  not  permitted  by  the 
contempt  or  the  supineness  of  his  enemies  to 
proceed  unmolested  in  making  proselytes ;  but 
was  actively  opposed  from  the  beginning  by  the 
priests  and  chief  men  of  the  national  religion ; 
was  repeatedly  in  danger  of  losing  his  life  ;  and 
after  a  short  ministry  of  three  years  duration  at 
the  utmost,  was  delivered  to  the  civil  power, 
and  crucified  as  a  malefactor.  Yet  notwith- 
standing this  event  the  progress  of  the  religion 
continued.  The  disciples  of  Christ,  though 
they  could  have  no  reason  to  expect  better 
treatment  than  their  master  had  received; 
though  they  expected,  as  they  had  been  taught 
by  him  and  professed  to  expect,  nothing  in  the 
present  life  but  troubles  and  persecutions,  per- 
severed in  preaching  the  same  religion  as  he 
had  taught,  with  this  additional  and  extraordi- 
nary circumstance  that  their  master,  on  the  third 
day  after  his  crucifixion,  had  arisen  from  the 
dead :  and  encountered  the  severest  punish- 
ments, and  death  Uself,  rather  than  cease  from 


396  THE  YOUNG  MECHANIC. 

publishing  and  attesting  doctrines  and  facts, 
which,  if  false,  they  could  not  but  know  to  be 
so ;-  and  from  the  preaching  of  which,  if  true, 
they  could  look  for  no  present  advantage.  And 
from  these  humble  beginnings,  and  by  these 
unpromising  methods,  did  Christianity  make  its 
way  so  successfully,  that  within  three  centuries 
from  the  first  preaching  of  Christ,  it  penetrated 
to  the  remotest  extremities  of  the  Roman  em- 
pire, and  established  itself  on  the  ruins  of  every 
other  religion  which  it  found  existing. 

When  all  these  circumstances  are  considered, 
and  they  are  such  as  unbelievers  in  general  are 
ready  to  admit,  it  seems  nearly  impossible  not 
to  come  to  the  following  conclusion : — that  a 
religion  of  such  an  origin,  and  avowedly  aiming 
at  such  objects;  a  religion  thus  destitute  of  all 
worldly  means  of  credit  and  support,  thus  pro- 
voking and  experiencing  every  kind  of  worldly 
opposition,  could  scarcely  ever  have  obtained 
beli»f  and  acceptation,  if  its  pretensions  had 
not  been  founded  on  irresistible  truth ;  and  con- 
sequently, that  its  establishment  under  all  these 
circumstances  affords  so  very  strong  a  presump- 
tion that  it  is  true,  as  necessarily  to  render  every 
competent  judge  to  whom  they  are  known,  and 
who  doubts  or  disbelieves  Christianity,  crimi- 


RELIGION.  3917 

nal  in  the  sight  of  God,  if  he  does  not  carefully 
examine  into  the  specific  evidence  by  which 
that  religion  is  supported. 

This  is  the  conclusion  to  which  it  has  been 
my  object  to  lead  by  fair  reasoning  the^canclid 
reader,  who  distrusts  or  denies  the  truth  of  the 
Christian  revelation.  If  this  conclusion  appears 
to  him  well  established,  he  will  naturally  seek 
for  a  detailed  account  of  the  evidence  of  the 
Christian  religion  in  treatises  written  professedly 
on  the  subject ;  and  will  make  himself  acquaint- 
ed with  the  many  striking  internal  proofs  which 
it  bears  of  its  own  authenticity,  by  a  diligent 
and  attentive  study  of  the  Scriptures.  And  let 
him  conduct  the  whole  of  his  investigations 
with  that  impartial  spirit  which  is  always  essen- 
tial to  the  discovery  of  the  truth,  whatever  be 
the  subject  under  discussion ;  guarding  against 
the  influence  of  former  prepossessions,  and 
former  practices,  with  a  degree  of  caution  and 
solicitude  proportioned  to  the  supreme  import 
ance  of  the  inquiry  in  which  he  is  engaged. 
Let  him  be  prepared  "  to  do  the  will  of  God ;" 
and  he  will  not  fail,  "  to  know  concerning  the 
doctrine  whether  it  be  of  God." 

I  would  in  the  next  place  offer  a  few  obser- 
vations to  the  consideration  of  those  believers 


398  THE  YOUNG  MECHANIC. 

in  Christianity,  who  contend  that  an  exact  ob* 
servance  of  all  its  precepts  is  more  than  is  now 
required  of  them. 

This  plea  for  deliberate  deviations  from  the 
strictness  of  obedience,  a  plea  which  we  more 
frequently  hear  obscurely  intimated  than  expli- 
citly stated,  appears,  when  unfolded,  to  resolve 
itself  into  the  following  assertions  : — that  if  the 
generality  of  men  would  act  in  scrupulous  con- 
formity to  the  precepts  of  Christianity,  no  in- 
dividual could  be  vindicated  were  he  to  conduct 
himself  otherwise ;  but  that  every  man  must 
take  the  world  as  it  is,  and  consider  what  is 
practicable  in  the  existing  state  of  things  :  that 
if  government,  for  example,  cannot  be  carried 
on  without  a  certain  degree  of  deceit  and  cor- 
ruption, the  politician  is  excusable  who  prac- 
tises it ;  that  if  men  in  trade  cannot  maintain 
their  station  without  using  the  same  objection- 
able arts  which  are  adopted  by  their  competi- 
tors, the  necessity  of  the  case  is  a  sufficient 
apology ;  that  similar  reasoning  is  applicable 
to  every  other  profession ;  that  extravagant  and 
needless,  latitude  would  certainly  be  unjustifi- 
able ;  but  that  it  is  absurd  to  require  points  of 
morality  to  be  pushed  to  extremes,  and  to  refuse 


-.2-JSJi^. 


RELIGION.  399 

to  make  necessary  allowances  for  compliance 
with  established  customs. 

Before  we  examine  what  countenance  the 
plea  in  question  meets  with  in  the  Scriptures, 
it  may  be  useful  to  inquire  whether  it  approves 
itself  to  sober  reason. 

Now,  since  they  who  allege  this  plea,  pro- 
fessedly make  the  degree  in  which  it  is  custo- 
mary for  men  to  deviate  from  the  rules  pre- 
scribed in  the  Gospel,  the  standard  measure  of 
the  degree  of  latitude  in  deviating  from  them 
which  each  individual  is  at  liberty  to  use ;  they 
must  unavoidably  admit,  if  they  will  reason  con- 
sistently with  their  own  principles,  that  when 
the  general  depravity  is  augmented  in  any  pro- 
portion, exactly  in  the  same  proportion  is  that 
latitude  augmented ;  and  consequently  that  a 
degree  of  latitude,  which  in  one  state  of  things 
they  pronounce  extravagant  and  unnecessary," 
may  become  highly  needful  and  proper  in 
another.  This  in  fact  is  to  affirm,  that  instead 
of  the  practice  of  men  being  rendered  conform- 
able to  the  laws  of  God,  the  degree  of  obe- 
dience due  from  any  man  to  those  laws  depends 
solely  on  the  practice  of  his  neighbours ;  and 
that  if  it  should  be  the  general  practice  utterly 
to  disregard  and  contemn  them,  no  individual 


400  TIIE  YOUNG  MECHANIC. 

would  be  under  any  obligations  to  pay  to  them 
the  slightest  attention  whatever.  If  an  argu- 
ment like  this,  which  strikes  directly  at  the  root 
of  all  religion,  cannot  be  maintained  by  those 
who  believe  in  Christianity;  neither  can  the 
plea  which  necessarily  involves  it. 

In  the  next  place,  does  this  plea  receive  more 
encouragement  from  the  Scriptures  ?  From  that 
quarter  it  experiences  nothing  but  repulse  and 
condemnation.  Those  who  urge  it  cannot  pro 
duce  one  single  text  authorizing  an  individual 
to  relax  in  his  obedience  to  the  precepts  of  the 
Gospel,  for  the  sake  of  escaping  difficulties  and 
losses,  through  fear  of  giving  offence,  through 
deference  to  custom  or  authority,  or  through 
any  worldly  motive  whatever.  What  is  the 
language  of  the  Old  and  New  Testaments  on 
the  subject  ?  u  Thou  shalt  not  follow  a  multi- 
tude to  do  evil." — "  Be  not  conformed  to  this 
world,"  (that  is,  to  the  evil  principles  and  prac- 
tises which  prevail  in  it,)  "but  be  transformed 
by  the  renewing  of  your  mind,  that  ye  may 
prove  what  is  that  good,  and  acceptable  and 
perfect  will  of  God." — "  Love  i  ot  the  world, 
neither  the  things  that  are  in  the  world.  If  any 
man  love  the  world,  the  love  of  the  Fathei  is 
not  in  him  Fo.r  all  that  is  in  the  world,  the 


RELIGION.  40} 

lust  of  the  flesh,  and  the  lust  of  the  eyes,  and 
the  pride  of  life,  is  not  of  the  Father,  but  is  of 
the  world.  And  the  world  passeth  away,  and 
the  lust  thereof :  but  he  that  doeth  the  will  of 
God  abide th  for  ever." — u  Be  ye  therefore  per- 
feet,  even  as  your  Father  which  is  in  Heaven  is 
perfect." — "  The  love  of  Christ  constraineth 
us,  because  we  thus  judge,  that  if  one  died  for 
all,  then  were  all  dead  :  and  that  he  died  for 
all,  that  they  which  live  should  henceforth  not 
live  unto  themselves,  but  unto  him  which  died 
for  them  and  rose  again." — "  What  shall  it  profit 
a  man,  if  he  shall  gain  the  whole  world,  and 
lose  his  own  soul  ?  Or  what  shall  a  man  give 
in  exchange  for  his  soul  ?  Whosoever  there- 
fore shall  be  ashamed  of  me,  and  of  my  words, 
in  this  adulterous  and  sinful  generation,  of  him 
also  shall  the  Son  of  man  be  ashamed,  when 
he  cometh  in  the  glory  of  his  Father  with  the 
holy  angels."  To  these  passages  are  to  be 
added  the  directions  incidently  given  by  St.  Paul 
to  persons  in  many  different  stations,  exhorting 
them  to  fulfil  the  respective  offices  peculiar  to 
those  stations  "  for  conscience  sake,  as  unto  the 
Lord,  and  not  unto  men ;"  directions  which, 
Dy  parity  of  reasoning  we  may  rest  assured 
that  the  apostle  would  have  applied  to  all  other 


402  THE  YOUNG  MECHANIC. 

situations  and  circumstances  of  life,  if  he  had 
been  led  by  his  subject  to  notice  them  distinctly 
And  lie  rJid  in  fact  make  the  application  univer- 
sal, when  he  delivered  these  general  and  com- 
prehensive precepts  :  "  Whatsoever  ye  do,  do 
all  to  the  glory  of  God." — "  Whatever  ye  do, 
in  word  or  in  deed,  do  all  in  the  name  of  the 
Lord  Jesus."  A  serious  desire  to  please  God 
in  all  we  do,  rendering  the  manner  of  pursuing 
the  business  of  our  calling,  be  it  what  it  may, 
one  of  the  expressions  of  that  desire,  is  the 
grand  principle  which  these  passages  inculcate ; 
and  it  is  the  principle  which,  beyond  all  others, 
I  could  wish  to  impress  on  the  mind  of  the 
reader,  whatever  be  his  station  or  profession,  as 
being  the  only  one  which  will  lead  him  steadily 
to  fix  his  attention  on  the  duties  which  he  has 
to  perform,  and  the  temptations  which  he  must 
encounter.  It  is  impossible  to  conceive  that  he 
who  knowingly  deviates  from  the  path  of  moral 
rectitude  and  Christian  duty,  because  most 
others  in  the  same  rank  and  profession  with 
himself  deviate  from  it,  and  because,  by  forbear- 
ing to  deviate,  he  should  incur  embarrassment 
and  losses,  odium  and  disgrace,  is,  in  that  in- 
stance, acting  consistently  with  the  letter  or  the 
spirit  of  the  various  scriptural  inj  unctions  which 


RELIGION.  403 

have  been  quoted.  Let  those  who  find  them- 
selves tempted  to  such  deviations,  consider 
whether  it  is  not  probable  that  the  Supreme 
Being,  on  whose  providence  the  success  of 
every  undertaking  depends,  will  prosper  those 
who  scrupulously  observe  the  laws  which  he 
has  prescribed  for  their  conduct,  and  leave  the 
issue  in  his  hands,  rather  than  those  who  mani- 
fest their  distrust  of  his  care  by  resorting  to 
arts  and  practices  which  he  has  forbidden ; 
whether  those  who  are  injured  in  their  worldly 
prospects  by  their  conscientious  adherence  to 
the  line  of  rectitude,  are  not  entitled  to  the  full 
benefit  of  the  scriptural  consolation,  u  If  ye 
suffer  for  righteousness  sake,  happy  are  ye  :" 
and  whether  it  is  not  the  part  of  wisdom  as 
well  as  of  duty,  whatever  be  the  event  at  pre- 
sent, to  regulate  every  action  by  that  rule,  ac- 
cording t,o  which  it  will  be  judged  at  the  last 
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